Systems of equations — find a variable Practice Questions (Grade 9)

Question 1easy

$\begin{cases} x = 4 \ 2x + 3y = 26 \end{cases}$
What is the $y$ -value of the solution to the system?

Substitute $x = 4$ into the second equation: $2(4) + 3y = 26$ , so $8 + 3y = 26$ , $3y = 18$ , and $y = 6$ .

Question 2easy

$\begin{cases} 3x + 2y = 28 \ x + y = 12 \end{cases}$
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 $x = 4$ .

Question 3easy

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

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

Question 4easy

$\begin{cases} x + 3y = 7 \ 2x + y = 9 \end{cases}$
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 $x = 4$ .

Question 5easy

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

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

Question 6easy

$\begin{cases} 5x + 2y = 25 \ x + y = 8 \end{cases}$
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 $x = 3$ .

Question 7easy

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

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

Question 8easy

$\begin{cases} y = 3x - 2 \ 2x + y = 18 \end{cases}$
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 practice