SAT (Scholastic Assessment Test) · Math

Systems of 2 linear equations in 2 variables: Practice Questions

5 multiple-choice questions marked as you go, and 3 written questions with worked solutions. All on Systems of 2 linear equations in 2 variables.

8 questions16 marksFree, no account

Question 1

1 mark

Consider the system of equations below:
\(2x + 3y = 12\)
\(y = 4 - \frac{2}{3}x\)
How many solutions \((x, y)\) does this system of equations have?

Question 2

1 mark

In the system of equations below, \( c \) is a constant. If the system has no solution, what is the value of \( c \)?
\( 5x - 2y = 10 \)
\( cx + 6y = 15 \)

Question 3

1 mark

What is the value of \( x \) in the solution to the system of equations below?
\( \frac{1}{2}x - \frac{1}{3}y = 5 \)
\( \frac{1}{4}x + \frac{2}{3}y = 10 \)

Question 4

1 mark

If \( y = 2x - 3 \) and \( x + y = 12 \), what is the value of \( x \)?

Question 5

1 mark

Consider the system of equations below:
\(3x + 2y = 16\)
\(x - y = 2\)
What is the value of \(y\) in the solution to this system?

Question 6

3 marks

If the system of linear equations \( 3x - 5y = 12 \) and \( kx + 10y = -24 \) has infinitely many solutions, what is the value of the constant \( k \)?

Write your answer out first, then check it against the worked solution.

Question 7

5 marks

In the system of equations below, \( c \) and \( d \) are constants. If the system has infinitely many solutions, what is the value of \( \frac{d}{c} \)?
\( 4x + cy = 10 \)
\( 12x + 9y = d \)

Write your answer out first, then check it against the worked solution.

Question 8

3 marks

In the system of equations below, what is the value of \( x + y \)?
\( 2x + 3y = 11 \)
\( 3x + 2y = 9 \)

Write your answer out first, then check it against the worked solution.

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