Algebra 2 Flashcards: Solving Systems Of Linear Equations

What this deck covers

This deck focuses on Solving Systems Of Linear Equations, giving you a quick way to review the definitions, rules, and examples that matter most for Algebra 2.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

Flashcard 1: What does it mean if a system of two linear equations has infinitely many solutions?

Answer: The lines coincide: equivalent equations for the same line. Every point on the line satisfies both equations.

Flashcard 2: What is the slope-intercept form of a linear equation?

Answer: $y=mx+b$. Standard form showing slope $m$ and $y$-intercept $b$.

Flashcard 3: What is the standard form of a linear equation used for elimination?

Answer: $Ax+By=C$. Format ideal for elimination method alignment.

Flashcard 4: Identify the condition for the same line in $y=mx+b$ form.

Answer: Equal slopes and intercepts: $m_1=m_2$ and $b_1=b_2$. Identical lines when both parameters match.

Flashcard 5: What is the solution of the system $y=\frac{1}{2}x+3$ and $y=-\frac{1}{2}x+1$?

Answer: $(-2,2)$. Set slopes equal: $\frac{1}{2}x+3=-\frac{1}{2}x+1$, solve.

Flashcard 6: What is the solution of the system $y=3x-5$ and $2y=6x-10$?

Answer: Infinitely many solutions (same line). Second equation is first multiplied by 2.

Flashcard 7: What is the solution of the system $y=3x-5$ and $2y=6x-10$?

Answer: Infinitely many solutions (same line). Second equation is first multiplied by 2.

Flashcard 8: What is the solution type for $y=2x+1$ and $y=2x-3$?

Answer: No solution (parallel lines). Same slope $m=2$, different intercepts.

Flashcard 9: What is the solution type for $2x+4y=8$ and $x+2y=4$?

Answer: Infinitely many solutions (equivalent equations). Second equation is first divided by 2.

Flashcard 10: What is the solution type for $3x-6y=9$ and $x-2y=5$?

Answer: No solution (parallel lines). Same slope $m=\frac{3}{2}$, different intercepts.

Flashcard 11: What method solves a system by making coefficients opposites and adding equations?

Answer: Elimination (linear combination). Add equations after making coefficients opposites.

Flashcard 12: What is the standard form of a linear equation used for elimination?

Answer: $Ax+By=C$. Format ideal for elimination method alignment.

Flashcard 13: What method solves a system by making coefficients opposites and adding equations?

Answer: Elimination (linear combination). Add equations after making coefficients opposites.

Flashcard 14: What method solves a system by solving one equation for a variable and substituting?

Answer: Substitution. Replace one variable with expression from other equation.

Flashcard 15: What method solves a system by finding the intersection point of two graphed lines?

Answer: Graphing (approximate intersection). Visual method showing where lines cross.

Flashcard 16: Identify the condition for parallel lines in $y=mx+b$ form.

Answer: Equal slopes $m_1=m_2$ and different intercepts $b_1\ne b_2$. Lines never meet when slopes match but intercepts differ.

Flashcard 17: Identify the system solution type if elimination gives a true statement like $0=0$.

Answer: Infinitely many solutions. Variables cancel to give identity $0=0$.

Flashcard 18: Identify the system solution type if elimination gives a false statement like $0=5$.

Answer: No solution. Variables cancel to give contradiction.

Flashcard 19: Identify the condition for the same line in $y=mx+b$ form.

Answer: Equal slopes and intercepts: $m_1=m_2$ and $b_1=b_2$. Identical lines when both parameters match.

Flashcard 20: What is the solution of the system $y=2x+1$ and $y=x+4$?

Answer: $(3,7)$. Set equations equal: $2x+1=x+4$, solve for $x=3$.

Flashcard 21: What is the slope of the line $3x-6y=12$?

Answer: $\frac{1}{2}$. Rewrite as $y=\frac{1}{2}x-2$ to find slope.

Flashcard 22: What is the solution of the system $y=-x+2$ and $y=x-4$?

Answer: $(3,-1)$. Set equations equal: $-x+2=x-4$, solve for $x=3$.

Flashcard 23: What is the solution of the system $3x-2y=4$ and $x+2y=8$?

Answer: $(3,\frac{5}{2})$. Add equations to eliminate $y$: $4x=12$, so $x=3$.

Flashcard 24: What is the solution of the system $x+y=10$ and $x-y=2$?

Answer: $(6,4)$. Add equations to get $2x=12$, so $x=6$.

Flashcard 25: What is the solution of the system $4x-y=9$ and $2x+y=3$?

Answer: $(2,-1)$. Add equations to eliminate $y$: $6x=12$, so $x=2$.

Flashcard 26: What is the solution of the system $5x+y=1$ and $x-y=7$?

Answer: $(\frac{4}{3},-\frac{17}{3})$. Add equations to eliminate $y$: $6x=8$, so $x=\frac{4}{3}$.

Flashcard 27: What is the solution of the system $y=\frac{1}{2}x+3$ and $y=-\frac{1}{2}x+1$?

Answer: $(-2,2)$. Set slopes equal: $\frac{1}{2}x+3=-\frac{1}{2}x+1$, solve.

Flashcard 28: What is the solution of the system $x=4$ and $y=-2x+1$?

Answer: $(4,-7)$. Substitute $x=4$ into second equation.

Flashcard 29: What is the solution of the system $y=6$ and $2x+y=10$?

Answer: $(2,6)$. Substitute $y=6$ into second equation.

Flashcard 30: What is the solution of the system $x+y=5$ and $2x+2y=8$?

Answer: No solution. Second equation gives $x+y=4$, contradicting first.