Solving Systems by Graphing - Pre Algebra

At what point do the lines $x = 4$ and $y = -1$ intersect?

$(4, -1)$ . One line is vertical and the other horizontal.
At what point do the lines $y = 3x - 2$ and $y = x + 4$ intersect?

$(3, 7)$ . Setting $3x - 2 = x + 4$ gives $x = 3$ , and then $y = 7$ .
Two phone plans are graphed as cost versus minutes. What does the intersection point mean?

The number of minutes at which both plans cost the same, and what that cost is.
How can you tell without graphing that $y = 2x + 1$ and $y = 2x - 3$ never meet?

They have the same slope and different $y$ -intercepts, so the lines are parallel and the system has no solution.
Graphing $y = 2x + 1$ and $y = -x + 7$ on the same grid, at which point do the lines meet?

$(2, 5)$ . Both equations give $y = 5$ when $x = 2$ , so that is the intersection.
How many solutions does a system have if both equations graph as the same line?

Infinitely many. Every point on the line satisfies both equations.
Why should a solution read from a graph be checked algebraically?

A graph can be read imprecisely, so substituting the point into both equations confirms it.
When two linear equations are graphed, what does their intersection point represent?

The solution of the system: the one ordered pair that makes both equations true.
How many solutions does a system have if its two lines are parallel?

None. Parallel lines never intersect.
At what point do the lines $y = 2x$ and $y = 6$ intersect?

$(3, 6)$ . Setting $2x = 6$ gives $x = 3$ .
In a graphed system, what does a point on only one of the two lines represent?

A solution of that one equation only. It is not a solution of the system.
At what point do the lines $y = x + 1$ and $y = -x + 5$ intersect?

$(2, 3)$ . Setting $x + 1 = -x + 5$ gives $x = 2$ , and then $y = 3$ .
How many times do two lines with different slopes intersect?

Exactly once, so the system has exactly one solution.

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