Solving systems of equations. Game on.

Solving systems of equations is a grade 9 math skill aligned to Common Core standard HSA.REI.C.6: solve systems of linear equations exactly and approximately, focusing on pairs of linear equations in two variables. Below are 8 practice questions with answers and step-by-step explanations, drawn from the 20 solving systems of equations problems our math games drill.

CCSS HSA.REI.C.620 questions in the bank
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Warm-upeasy

{y=x+3x+y=9\begin{cases} y = x + 3 \\ x + y = 9 \end{cases}
What is the solution (x,y)(x, y) to the given system of equations?

Solve using substitution.
y=x+3x+y =9x+(x+3)=92x+3=92x=6x=3y=x+3y=3+3y=6The solution is (3,6).\begin{aligned}&y=\textcolor{red}{x+3} \\ &x\textcolor{red}{+y}\,=9 \\ & \\ &x+\textcolor{red}{(x+3)}=9 \\ &2x+3=9 \\ &2x=6 \\ &x=3 \\ & \\ &y=\textcolor{blue}{x}+3 \\ &y=\textcolor{blue}{3}+3 \\ &y=6 \qquad \text{The solution is }(3, 6)\textsf{.}\end{aligned}

Mid-gameeasy

{x+y=5x−y=−1\begin{cases} x + y = 5 \\ x - y = -1 \end{cases}
What is the solution (x,y)(x, y) to the given system of equations?

Solve using elimination.
x+y=5x−y=−12x=5+(−1)2x=4x=2x+y=52+y=5y=3The solution is (2,3).\begin{aligned}&x\textcolor{red}{+y}=5 \\ &x\textcolor{red}{-y}=-1 \\ & \\ &2x=5+(-1) \\ &2x=4 \\ &x=2 \\ & \\ &\textcolor{blue}{x}+y=5 \\ &\textcolor{blue}{2}+y=5 \\ &y=3 \qquad \text{The solution is }(2, 3)\textsf{.}\end{aligned}

Mid-gameeasy

{y=3xy=x+10\begin{cases} y = 3x \\ y = x + 10 \end{cases}
What is the solution (x,y)(x, y) to the given system of equations?

Solve using substitution.
y=3xy=x+103x=x+103x=x+102x=10x=5y=3xy=3(5)y=15The solution is (5,15).\begin{aligned}&y=\textcolor{red}{3x} \\ &y=\textcolor{red}{x+10} \\ & \\ &\textcolor{red}{3x}=\textcolor{red}{x+10} \\ &3x=x+10 \\ &2x=10 \\ &x=5 \\ & \\ &y=3\textcolor{blue}{x} \\ &y=3\textcolor{blue}{(5)} \\ &y=15 \qquad \text{The solution is }(5, 15)\textsf{.}\end{aligned}

Mid-gameeasy

{x+y=10x−y=−2\begin{cases} x + y = 10 \\ x - y = -2 \end{cases}
What is the solution (x,y)(x, y) to the given system of equations?

Solve using elimination.
x+y=10x−y=−22x=10+(−2)2x=8x=4x+y=104+y=10y=6The solution is (4,6).\begin{aligned}&x\textcolor{red}{+y}=10 \\ &x\textcolor{red}{-y}=-2 \\ & \\ &2x=10+(-2) \\ &2x=8 \\ &x=4 \\ & \\ &\textcolor{blue}{x}+y=10 \\ &\textcolor{blue}{4}+y=10 \\ &y=6 \qquad \text{The solution is }(4, 6)\textsf{.}\end{aligned}

Mid-gameeasy

{y=2x+33x+y=18\begin{cases} y = 2x + 3 \\ 3x + y = 18 \end{cases}
What is the solution (x,y)(x, y) to the given system of equations?

Solve using substitution.
y=2x+33x+y=183x+(2x+3)=185x+3=185x=15x=3y=2x+3y=2(3)+3y=6+3y=9The solution is (3,9).\begin{aligned}&y=\textcolor{red}{2x+3} \\ &3x\textcolor{red}{+y}=18 \\ & \\ &3x+\textcolor{red}{(2x+3)}=18 \\ &5x+3=18 \\ &5x=15 \\ &x=3 \\ & \\ &y=2\textcolor{blue}{x}+3 \\ &y=2\textcolor{blue}{(3)}+3 \\ &y=6+3 \\ &y=9 \qquad \text{The solution is }(3, 9)\textsf{.}\end{aligned}

Mid-gameeasy

{x+y=−5x−y=−3\begin{cases} x + y = -5 \\ x - y = -3 \end{cases}
What is the solution (x,y)(x, y) to the given system of equations?

Solve using elimination.
x+y=−5x−y=−32x=−5+(−3)2x=−8x=−4x+y=−5(−4)+y=−5y=−1The solution is (−4,−1).\begin{aligned}&x\textcolor{red}{+y}=-5 \\ &x\textcolor{red}{-y}=-3 \\ & \\ &2x=-5+(-3) \\ &2x=-8 \\ &x=-4 \\ & \\ &\textcolor{blue}{x}+y=-5 \\ &\textcolor{blue}{(-4)}+y=-5 \\ &y=-1 \qquad \text{The solution is }(-4, -1)\textsf{.}\end{aligned}

Mid-gameeasy

{y=−x+8y=2x−1\begin{cases} y = -x + 8 \\ y = 2x - 1 \end{cases}
What is the solution (x,y)(x, y) to the given system of equations?

Solve using substitution.
y=−x+8y=2x−1−x+8=2x−1−x+8=2x−18+1=2x+x9=3xx=3y=2x−1y=2(3)−1y=6−1y=5The solution is (3,5).\begin{aligned}&y=\textcolor{red}{-x+8} \\ &y=\textcolor{red}{2x-1} \\ & \\ &\textcolor{red}{-x+8}=\textcolor{red}{2x-1} \\ &-x+8=2x-1 \\ &8+1=2x+x \\ &9=3x \\ &x=3 \\ & \\ &y=2\textcolor{blue}{x}-1 \\ &y=2\textcolor{blue}{(3)}-1 \\ &y=6-1 \\ &y=5 \qquad \text{The solution is }(3, 5)\textsf{.}\end{aligned}

Buzzer beatereasy

{x+y=3x−y=−5\begin{cases} x + y = 3 \\ x - y = -5 \end{cases}
What is the solution (x,y)(x, y) to the given system of equations?

Solve using elimination.
x+y=3x−y=−52x=3+(−5)2x=−2x=−1x+y=3(−1)+y=3y=4The solution is (−1,4).\begin{aligned}&x\textcolor{red}{+y}=3 \\ &x\textcolor{red}{-y}=-5 \\ & \\ &2x=3+(-5) \\ &2x=-2 \\ &x=-1 \\ & \\ &\textcolor{blue}{x}+y=3 \\ &\textcolor{blue}{(-1)}+y=3 \\ &y=4 \qquad \text{The solution is }(-1, 4)\textsf{.}\end{aligned}

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Tests that cover solving systems of equations:
PSAT 8/9SATNAEPNY State MathMCAP
Reporting domains for this skill
SAT All grades: AlgebraACT All grades: Preparing for Higher MathSTAAR Algebra I: Number and Algebraic MethodsMAP Growth Math 6+: Operations and Algebraic ThinkingNAEP Grade 12: AlgebraACT Aspire All grades: Preparing for Higher Math
More Grade 9 skills
Systems word problems with one value givenSystems of equations — find a variableSquare and cube binomialsSystems by simple substitutionSolving systems that compare numbersSolving quadratics (leading coefficient not 1)Writing a two-variable equation from contextSlope-point line equations (ACT/SAT/PSAT 8/9/10)All Grade 9 practice →

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