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

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Practice 82 Systems of two linear equations in two variables questions in the app

What this topic is

Systems of two linear equations in two variables on SAT Math covers finding the ordered pair that satisfies both equations, plus the cases of no solution and infinitely many solutions.

Sample questions

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

Question 1Easier

$4x+3y=53$

$3x+2y=34$

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

A$-53$✗ Not this oneB$-19$✗ Not this oneC19✓ CorrectD53✗ Not this one

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Answer: C — 19

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

Question 2Easier

$7x+3y=-11$

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?

A$14x+6y=-11$✗ Not this oneB$-21x-9y=33$✓ CorrectC$7x-3y=-11$✗ Not this oneD$21x+9y=33$✗ Not this one

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Answer: B — $-21x-9y=33$

Multiplying $7x+3y=-11$ by $-3$ produces $-21x-9y=33$. 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?

A18✗ Not this oneB28✗ Not this oneC32✗ Not this oneD37✓ Correct

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Answer: D — 37

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

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