SAT Systems Of Linear Equations Practice Questions (Free + Explanations)

Algebra · Systems Of Linear Equations

SAT Systems Of Linear Equations Practice Questions (Free + Explanations) | Quiz 1

Question 12345 of 5

Question 1 of 5

At a school fundraiser, adult tickets cost 8 each and student tickets cost 5 each. A total of 27 tickets were sold for 171 . How many adult tickets were sold?

Explanation Let a be the number of adult tickets and s be the number of student tickets. The problem gives the system a + s = 27 8 a + 5 s = 171 Since a + s = 27, we have s = 27 - a . Substitute into the revenue equation: 8 a + 5 (27 - a) = 171 8 a + 135 - 5 a = 171 3 a = 36 a = 12 So, 12 adult tickets were sold. Concept summary A system of linear equations can model a situation with two unknown quantities, such as the number of each type of ticket sold.

Question 2 of 5

If the system of equations x + y = 14 and x - y = 2 is true, what is the value of x ?

Explanation Add the two equations to eliminate y : x + y + x - y = 14 + 2 so 2 x = 16 . Dividing by 2 gives x = 8 . Concept summary In a system of linear equations, adding or subtracting the equations can eliminate one variable and make the other easy to solve.

Question 3 of 5

The system of equations x + y = 12 and x - y = 4 has solution (x, y) . Which expression is equivalent to the value of x ?

Explanation Add the two equations: (x + y) + (x - y) = 12 + 4. This gives 2 x = 16, so x = \frac{16}{2} = \frac{12 + 4}{2} . Concept summary In a system with one sum equation and one difference equation, adding the equations eliminates one variable and can create an equivalent expression for the other variable.

Question 4 of 5

In the x y -plane, two lines intersect at the point (3, 2) . Which system of equations could represent these lines?

Explanation The intersection point of a system is the point that makes both equations true. Substitute (3, 2) into each pair. For y = x - 1, 2 = 3 - 1, which is true. For y = - x + 5, 2 = - 3 + 5, which is also true. So this system could represent two lines that intersect at (3, 2) . Concept summary For a system of linear equations, the intersection point must satisfy both equations at the same time.

Question 5 of 5

The system of equations y = 2 x + 1 and y = 7 has solution (x, y) . What is the value of x ?

Explanation Since both equations equal y, set them equal to each other: 2 x + 1 = 7 . Then 2 x = 6, so x = 3 . Concept summary In a system, if two expressions are both equal to the same variable, set them equal to each other to solve for the unknown.

Your results

0of 5 correct

Estimated SAT Math band

500-550

Illustrative range from this short quiz—not an official College Board score.

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Your results

1of 5 correct

Estimated SAT Math band

500-550

Illustrative range from this short quiz—not an official College Board score.

Adaptive practice, weak-area review, and timed tests live in the MCQsLearn app—pick up where you left off on your phone.

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More SAT Math practice

Your results

2of 5 correct

Estimated SAT Math band

600-650

Illustrative range from this short quiz—not an official College Board score.

Adaptive practice, weak-area review, and timed tests live in the MCQsLearn app—pick up where you left off on your phone.

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More SAT Math practice

Your results

3of 5 correct

Estimated SAT Math band

600-650

Illustrative range from this short quiz—not an official College Board score.

Adaptive practice, weak-area review, and timed tests live in the MCQsLearn app—pick up where you left off on your phone.

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More SAT Math practice

Your results

4of 5 correct

Estimated SAT Math band

700+

Illustrative range from this short quiz—not an official College Board score.

Adaptive practice, weak-area review, and timed tests live in the MCQsLearn app—pick up where you left off on your phone.

Download on the App Store Get it on Google Play

More SAT Math practice

Your results

5of 5 correct

Estimated SAT Math band

700+

Illustrative range from this short quiz—not an official College Board score.

Adaptive practice, weak-area review, and timed tests live in the MCQsLearn app—pick up where you left off on your phone.

Download on the App Store Get it on Google Play

More SAT Math practice

Practice outline (enable JavaScript for interactive mode)

Q1. At a school fundraiser, adult tickets cost 8 each and student tickets cost 5 each. A total of 27 tickets were sold for 171 . How many adult tickets were sold?

Q2. If the system of equations x + y = 14 and x − y = 2 is true, what is the value of x ?

Q3. The system of equations x + y = 12 and x − y = 4 has solution ( x , y ) . Which expression is equivalent to the value of x ?

Q4. In the x y -plane, two lines intersect at the point ( 3 , 2 ) . Which system of equations could represent these lines?

Q5. The system of equations y = 2 x + 1 and y = 7 has solution ( x , y ) . What is the value of x ?