This question tests understanding that a system solution is the intersection point of graphs—the (x,y) satisfying both equations simultaneously shown where lines cross. Two linear equations graph as two lines; solution is where lines intersect (point on both lines): one intersection (different slopes, one solution), parallel (same slope different intercepts, no intersection/no solution), or same line (infinite points/infinite solutions). Point (x,y) is solution if substituting into both equations gives true statements (x=3, y=5 in y=3x-4: 5=3(3)-4=5✓, and y=-x+8: 5=-(3)+8=5✓, both true so (3,5) solves system). To verify, set 3x-4 = -x+8, yielding 4x=12 so x=3, then y=5, confirming (3,5) as the intersection. The correct choice is A, as C reverses coordinates, and B and D are points not on both lines. Strategy: (1) graph both equations (or interpret given graph), (2) identify intersection (where lines cross, read coordinates), (3) verify algebraically (substitute x,y into both equations checking both true), (4) classify (intersecting once=one solution, parallel=no solution, same line=infinite). Connection: graph is visual (see solution location), algebra is exact (calculate precise coordinates), both show same information (intersection point = system solution). Mistakes: checking only one equation (must verify both), reading coordinates wrong (x,y order matters), claiming parallel lines meet.

This question tests understanding that a system solution is the intersection point of graphs—the (x,y) satisfying both equations simultaneously shown where lines cross. Two linear equations graph as two lines; solution is where lines intersect (point on both lines): one intersection (different slopes, one solution), parallel (same slope different intercepts, no intersection/no solution), or same line (infinite points/infinite solutions). Point (x,y) is solution if substituting into both equations gives true statements (x=4, y=3 in $y=\frac{1}{2}x+1$: $3=\frac{1}{2}(4)+1=3$ ✓, and $y=-x+7$: $3=-(4)+7=3$ ✓, both true so (4,3) solves system). Verification shows both equations hold true for (4,3), so it is the intersection point. The correct choice is A, as B checks only one, C incorrectly claims second false, and D says both false. Strategy: (1) graph both equations (or interpret given graph), (2) identify intersection (where lines cross, read coordinates), (3) verify algebraically (substitute x,y into both equations checking both true), (4) classify (intersecting once=one solution, parallel=no solution, same line=infinite). Connection: graph is visual (see solution location), algebra is exact (calculate precise coordinates), both show same information (intersection point = system solution). Mistakes: checking only one equation (must verify both), reading coordinates wrong (x,y order matters), claiming parallel lines meet.

This question tests understanding that a system solution is the intersection point of graphs—the (x,y) satisfying both equations simultaneously shown where lines cross. Two linear equations graph as two lines; solution is where lines intersect (point on both lines): one intersection (different slopes, one solution), parallel (same slope different intercepts, no intersection/no solution), or same line (infinite points/infinite solutions). Point (x,y) is solution if substituting into both equations gives true statements (x=2, y=5 in y=2x+1: 5=2(2)+1=5✓, and y=-x+7: 5=-(2)+7=5✓, both true so (2,5) solves system). To verify, set 2x+1 = -x+7, yielding 3x=6 so x=2, then y=5, confirming (2,5) as the intersection. The correct choice is B, as A reverses coordinates, C has wrong y, and D is unrelated. Strategy: (1) graph both equations (or interpret given graph), (2) identify intersection (where lines cross, read coordinates), (3) verify algebraically (substitute x,y into both equations checking both true), (4) classify (intersecting once=one solution, parallel=no solution, same line=infinite). Connection: graph is visual (see solution location), algebra is exact (calculate precise coordinates), both show same information (intersection point = system solution). Mistakes: checking only one equation (must verify both), reading coordinates wrong (x,y order matters), claiming parallel lines meet.

Tests understanding system solution is intersection point of graphs—the $(x,y)$ satisfying both equations simultaneously shown where lines cross. Two linear equations graph as two lines; solution is where lines intersect (point on both lines): one intersection (different slopes, one solution), parallel (same slope different intercepts, no intersection/no solution), or same line (infinite points/infinite solutions). Point $(x,y)$ is solution if substituting into both equations gives true statements (x=2, y=5 in $y=2x+1$: $5=2(2)+1=5$✓, and $y=-x+7$: $5=-(2)+7=5$✓, both true so $(2,5)$ solves system). The system has lines with slopes 2 and -1, different, so they intersect at one point, found by solving $2x+1=-x+7$ yielding $x=2$, $y=5$. The correct solution is $(2,5)$, which is the intersection point. A common error is reversing coordinates to get (5,2) or misreading the point. Strategy: (1) graph both equations (or interpret given graph), (2) identify intersection (where lines cross, read coordinates), (3) verify algebraically (substitute x,y into both equations checking both true), (4) classify (intersecting once=one solution, parallel=no solution, same line=infinite). Connection: graph is visual (see solution location), algebra is exact (calculate precise coordinates), both show same information (intersection point = system solution). Mistakes: checking only one equation (must verify both), reading coordinates wrong (x,y order matters), claiming parallel lines meet.

Tests understanding system solution is intersection point of graphs—the (x,y) satisfying both equations simultaneously shown where lines cross. Two linear equations graph as two lines; solution is where lines intersect (point on both lines): one intersection (different slopes, one solution), parallel (same slope different intercepts, no intersection/no solution), or same line (infinite points/infinite solutions). Point (x,y) is solution if substituting into both equations gives true statements (x=2, y=4 in y=x+2: $4=2+2=4$ ✓, and y=6-x: $4=6-2=4$ ✓, both true; but (1,5): $5=1+2=3$ ✗, though $5=6-1=5$ ✓, so only one true). The system intersects at (2,4), so points like (1,5) do not satisfy both equations. Any point not at the intersection, such as (1,5), is not a solution. A common error is checking only one equation, thinking a point on one line solves the system. Strategy: (1) graph both equations (or interpret given graph), (2) identify intersection (where lines cross, read coordinates), (3) verify algebraically (substitute x,y into both equations checking both true), (4) classify (intersecting once=one solution, parallel=no solution, same line=infinite). Connection: graph is visual (see solution location), algebra is exact (calculate precise coordinates), both show same information (intersection point = system solution). Mistakes: checking only one equation (must verify both), reading coordinates wrong (x,y order matters), claiming parallel lines meet.

Tests understanding system solution is intersection point of graphs—the ($x,y$) satisfying both equations simultaneously shown where lines cross. Two linear equations graph as two lines; solution is where lines intersect (point on both lines): one intersection (different slopes, one solution), parallel (same slope $3$ but different intercepts $2$ and $-1$, no intersection/no solution), or same line (infinite points/infinite solutions). Point ($x,y$) is solution if substituting into both equations gives true statements (for example, trying to set $3x+2=3x-1$ yields $2=-1$, false, so no solution). The system has lines with same slope $3$ but different intercepts $2$ and $-1$, so they are parallel and do not intersect. The correct classification is no solutions, as parallel lines never cross. A common error is claiming they intersect despite same slope or wrong arithmetic in checking consistency. Strategy: (1) graph both equations (or interpret given graph), (2) identify intersection (where lines cross, read coordinates), (3) verify algebraically (substitute $x,y$ into both equations checking both true), (4) classify (intersecting once=one solution, parallel=no solution, same line=infinite). Connection: graph is visual (see solution location), algebra is exact (calculate precise coordinates), both show same information (intersection point = system solution). Mistakes: checking only one equation (must verify both), reading coordinates wrong ($x,y$ order matters), claiming parallel lines meet.

This question tests understanding that a system solution is the intersection point of graphs—the (x,y) satisfying both equations simultaneously shown where lines cross. Two linear equations graph as two lines; solution is where lines intersect (point on both lines): one intersection (different slopes, one solution), parallel (same slope different intercepts, no intersection/no solution), or same line (infinite points/infinite solutions). Line 1 is y=-x+6, Line 2 is y=2x; setting equal gives -x+6=2x so x=2, y=4, confirming (2,4). Verification: (2,4) satisfies both equations, as slopes differ (-1 and 2). The correct choice is B, as A, C, D are points on one line only or endpoints. Strategy: (1) graph both equations (or interpret given graph), (2) identify intersection (where lines cross, read coordinates), (3) verify algebraically (substitute x,y into both equations checking both true), (4) classify (intersecting once=one solution, parallel=no solution, same line=infinite). Connection: graph is visual (see solution location), algebra is exact (calculate precise coordinates), both show same information (intersection point = system solution). Mistakes: checking only one equation (must verify both), reading coordinates wrong (x,y order matters), claiming parallel lines meet.

Tests understanding system solution is intersection point of graphs—the (x,y) satisfying both equations simultaneously shown where lines cross. Two linear equations graph as two lines; solution is where lines intersect (point on both lines): one intersection (different slopes, one solution), parallel (same slope different intercepts, no intersection/no solution), or same line (infinite points/infinite solutions). Point (x,y) is solution if substituting into both equations gives true statements (for lines with slopes 1/2 and -1/2, different, they intersect at one point satisfying both). The intersection point represents the (x,y) that solves the system, being on both lines. The correct interpretation is a point that makes both equations true at the same time. A common error is thinking it's just on one line or confusing with intercepts. Strategy: (1) graph both equations (or interpret given graph), (2) identify intersection (where lines cross, read coordinates), (3) verify algebraically (substitute x,y into both equations checking both true), (4) classify (intersecting once=one solution, parallel=no solution, same line=infinite). Connection: graph is visual (see solution location), algebra is exact (calculate precise coordinates), both show same information (intersection point = system solution). Mistakes: checking only one equation (must verify both), reading coordinates wrong (x,y order matters), claiming parallel lines meet.

This question tests understanding that a system solution is the intersection point of graphs—the (x,y) satisfying both equations simultaneously shown where lines cross. Two linear equations graph as two lines; solution is where lines intersect (point on both lines): one intersection (different slopes, one solution), parallel (same slope different intercepts, no intersection/no solution), or same line (infinite points/infinite solutions). Point (x,y) is solution if substituting into both equations gives true statements (x=2, y=5 in y=2x+1: 5=2(2)+1=5✓, and y=-x+7: 5=-(2)+7=5✓, both true so (2,5) solves system). To verify, set 2x+1 = -x+7, yielding 3x=6 so x=2, then y=5, confirming (2,5) as the intersection. The correct choice is B, as A reverses coordinates, C has wrong y, and D is unrelated. Strategy: (1) graph both equations (or interpret given graph), (2) identify intersection (where lines cross, read coordinates), (3) verify algebraically (substitute x,y into both equations checking both true), (4) classify (intersecting once=one solution, parallel=no solution, same line=infinite). Connection: graph is visual (see solution location), algebra is exact (calculate precise coordinates), both show same information (intersection point = system solution). Mistakes: checking only one equation (must verify both), reading coordinates wrong (x,y order matters), claiming parallel lines meet.

This question tests understanding that a system solution is the intersection point of graphs—the (x,y) satisfying both equations simultaneously shown where lines cross. Two linear equations graph as two lines; solution is where lines intersect (point on both lines): one intersection (different slopes, one solution), parallel (same slope different intercepts, no intersection/no solution), or same line (infinite points/infinite solutions). Point (x,y) is solution if substituting into both equations gives true statements (x=3, y=5 in $y=3x-4$: $5=3(3)-4=5$✓, and $y=-x+8$: $5=-(3)+8=5$✓, both true so (3,5) solves system). To verify, set $3x-4 = -x+8$, yielding $4x=12$ so $x=3$, then $y=5$, confirming (3,5) as the intersection. The correct choice is A, as C reverses coordinates, and B and D are points not on both lines. Strategy: (1) graph both equations (or interpret given graph), (2) identify intersection (where lines cross, read coordinates), (3) verify algebraically (substitute x,y into both equations checking both true), (4) classify (intersecting once=one solution, parallel=no solution, same line=infinite). Connection: graph is visual (see solution location), algebra is exact (calculate precise coordinates), both show same information (intersection point = system solution). Mistakes: checking only one equation (must verify both), reading coordinates wrong (x,y order matters), claiming parallel lines meet.