Systems of two linear equations in two variables — SAT practice questions

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Practice 88 Systems of two linear equations in two variables questions in the app

What this topic is

Systems of two linear equations in two variables ask for the point where two lines meet, found by substitution or elimination.

Many questions do not require both values: if the question asks for x + y, adding or subtracting the equations can produce it directly. Parallel lines, with equal slopes and different intercepts, give no solution, while equations that are multiples of each other describe the same line and give infinitely many.

Word problems usually involve two kinds of item with a known total count and a known total value, such as tickets at two prices, producing one equation for each total.

Sample questions

Pick an answer to see whether it is right — nothing is saved, and nothing needs an account.

Question 1Easier

4 x + 3 y = 53

3 x + 2 y = 34

The solution to the given system of equations is $(x, y)$ . What is the value of $x + y$ ?

- 53

✗ Not this one

- 19

✗ Not this one19✓ Correct53✗ Not this one

Show answer

Answer: C — 19

Subtracting the second equation from the first gives $(4 x + 3 y) - (3 x + 2 y) = 53 - 34$ , so $x + y = 19$ .

Question 2Easier

7 x + 3 y = - 11

The given equation is one equation in a system of two linear equations. If the system has infinitely many solutions, which of the following equations could be the other equation in the system?

14 x + 6 y = - 11

✗ Not this one

- 21 x - 9 y = 33

✓ Correct

7 x - 3 y = - 11

✗ Not this one

21 x + 9 y = 33

✗ Not this one

Show answer

Answer: B — $- 21 x - 9 y = 33$

Multiplying $7 x + 3 y = - 11$ by $- 3$ produces $- 21 x - 9 y = 33$ . The equations therefore describe the same line, so every point on that line is a solution.

Question 3Easier

A campus shop sold pens for $2 each and notebooks for $3 each. Yesterday the shop sold a combined total of 55 pens and notebooks for $128. How many pens were sold?

18✗ Not this one28✗ Not this one32✗ Not this one37✓ Correct

Show answer

Answer: D — 37

Let $p$ be pens and $n$ notebooks. Then $p + n = 55$ and $2 p + 3 n = 128$ . Substitute $n = 55 - p$ : $2 p + 3 (55 - p) = 128$ → $2 p + 165 - 3 p = 128$ → $- p = - 37$ → $p = 37$ .

Every question is picked for where you are right now, wrong answers come back until they stick, and it all works offline.

Practice 88 Systems of two linear equations in two variables questions in the app

Systems of two linear equations in two variables — SAT practice questions

What this topic is

Sample questions

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Math