Systems of equations — find a variable Practice Questions

Systems of equations — find a variable. Game on.

Systems of equations — find a variable 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 15 systems of equations — find a variable problems our math games drill.

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Warm-upeasy

$\begin{cases} x = 6 \\ 5x + 2y = 52 \end{cases}$
What is the $y$ -value of the solution to the system?

Substitute $x = 6$ into the second equation: $5(6) + 2y = 52$ , so $30 + 2y = 52$ , $2y = 22$ , and $y = 11$ .

Mid-gameeasy

$\begin{cases} 3x + 2y = 28 \\ x + y = 12 \end{cases}$
What is the $x$ -value of the solution to the system?

Multiply the second equation by $3$ : $3x + 3y = 36$ . Subtract the first equation: $y = 8$ . Substitute into $x + y = 12$ to get $x = 4$ .

Mid-gameeasy

$\begin{cases} x + 2y = 13 \\ x - 2y = 1 \end{cases}$
What is the $y$ -value of the solution to the system?

Subtract the second equation from the first: $4y = 12$ , so $y = 3$ .

Mid-gameeasy

$\begin{cases} x + 3y = 7 \\ 2x + y = 9 \end{cases}$
What is the $x$ -value of the solution to the system?

Multiply the second equation by $-3$ : $-6x - 3y = -27$ . Add the first equation: $-5x = -20$ , so $x = 4$ .

Mid-gameeasy

$\begin{cases} 4x + 3y = 25 \\ 4x - 3y = 7 \end{cases}$
What is the $y$ -value of the solution to the system?

Subtract the second equation from the first: $6y = 18$ , so $y = 3$ .

Mid-gameeasy

$\begin{cases} 5x + 2y = 25 \\ x + y = 8 \end{cases}$
What is the $x$ -value of the solution to the system?

Multiply the second equation by $-2$ : $-2x - 2y = -16$ . Add the first equation: $3x = 9$ , so $x = 3$ .

Mid-gameeasy

$\begin{cases} 2x + 5y = 29 \\ 2x + y = 9 \end{cases}$
What is the $y$ -value of the solution to the system?

Subtract the second equation from the first: $4y = 20$ , so $y = 5$ .

Buzzer beatereasy

$\begin{cases} y = 3x - 2 \\ 2x + y = 18 \end{cases}$
What is the $y$ -value of the solution to the system?

Substitute $y = 3x - 2$ into the second equation: $2x + 3x - 2 = 18$ , so $5x = 20$ , $x = 4$ , and $y = 10$ .

Systems of equations — find a variable. Game on.

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