Linear system expressions Practice Questions (Grade 9)

Question 1easy

$\begin{cases} 2x + y = 9 \ x - y = 3 \end{cases}$
The solution to this system is $(x, y)$ . What is the value of $x + 3y$ ?

Add the equations: $3x = 12$ , so $x = 4$ . From $x - y = 3$ , $y = 1$ . Then $x + 3y = 4 + 3 = 7$ .

Question 2easy

$\begin{cases} 3x = 21 \ 2x + y = 19 \end{cases}$
The solution to this system is $(x, y)$ . What is the value of $y - x$ ?

From $3x = 21$ , $x = 7$ . Substitute into the second equation: $14 + y = 19$ , so $y = 5$ . Then $y - x = 5 - 7 = -2$ .

Question 3medium

$\begin{cases} 4x + y = 15 \ 2x - y = 3 \end{cases}$
The solution to this system is $(x, y)$ . What is the value of $2x + 3y$ ?

Add the equations: $6x = 18$ , so $x = 3$ . From $4x + y = 15$ , $y = 3$ . Then $2x + 3y = 6 + 9 = 15$ .

Question 4medium

$\begin{cases} y = 2x - 1 \ 3x + y = 14 \end{cases}$
The solution to this system is $(x, y)$ . What is the value of $x - y$ ?

Substitute $y = 2x - 1$ into the second equation: $3x + 2x - 1 = 14$ , so $5x = 15$ and $x = 3$ . Then $y = 5$ , and $x - y = 3 - 5 = -2$ .

Question 5medium

$\begin{cases} 5x + 2y = 22 \ 3x + 2y = 18 \end{cases}$
The solution to this system is $(x, y)$ . What is the value of $3x + y$ ?

Subtract the second equation from the first: $2x = 4$ , so $x = 2$ . From $3x + 2y = 18$ , $6 + 2y = 18$ , so $y = 6$ . Then $3x + y = 6 + 6 = 12$ .

Question 6medium

$\begin{cases} 6x - y = 17 \ 2x + y = 7 \end{cases}$
The solution to this system is $(x, y)$ . What is the value of $4x + y$ ?

Add the equations: $8x = 24$ , so $x = 3$ . From $2x + y = 7$ , $y = 1$ . Then $4x + y = 12 + 1 = 13$ .

Question 7medium

$\begin{cases} -3x + y = 1 \ 2x + y = 11 \end{cases}$
The solution to this system is $(x, y)$ . What is the value of $3x - 2y$ ?

Subtract the first equation from the second: $5x = 10$ , so $x = 2$ . From $-3x + y = 1$ , $y = 7$ . Then $3x - 2y = 6 - 14 = -8$ .

Question 8medium

$\begin{cases} x + 4y = 18 \ 3x - 4y = 6 \end{cases}$
The solution to this system is $(x, y)$ . What is the value of $2x - y$ ?

Add the equations: $4x = 24$ , so $x = 6$ . From $x + 4y = 18$ , $y = 3$ . Then $2x - y = 12 - 3 = 9$ .

Linear system expressions practice