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Algebra · Systems Of Linear Equations

SAT Systems Of Linear Equations Practice Questions (Free + Explanations) | Quiz 9

Question 12345 of 5

Question 1 of 5

A system of two linear equations has the same solution as the system below.

Which statement must be true?

Explanation

The second equation is just times the first equation:

So both equations represent the same line. When two equations in a system represent the same line, every point on that line satisfies both equations. That means the system has infinitely many solutions.

Concept summary

In a system of linear equations, if one equation is a constant multiple of the other, the equations represent the same line and the system has infinitely many solutions.

Question 2 of 5

A school is selling tickets to a play. Student tickets cost \8\ each. On Friday, the school sold a total of tickets and collected \1{,}80015

Explanation

Let be the number of student tickets sold on Friday and be the number of adult tickets sold on Friday. Then

and

Substitute into the revenue equation:

So on Friday, adult tickets and student tickets were sold.

On Saturday, the number of adult tickets was more, so adult tickets sold was

Since the total number of tickets was still , student tickets sold was

Saturday's revenue was

So the school collected \1{,}890

Concept summary

Model the situation with a system for one day, solve for the original counts, then adjust one variable while keeping the total fixed to find the new revenue.

Question 3 of 5

A school sells tickets to a play. Student tickets cost \6\ each. On Friday, the school sold a total of tickets and collected \1{,}3202010

Explanation

Let be the number of student tickets sold on Friday and be the number of adult tickets sold on Friday. Then

and

Substitute into the revenue equation:

So . On Saturday, the school sold student tickets and adult tickets. The total money collected was

So the school collected \1{,}340

Concept summary

Model the situation with a system of linear equations, solve for the original quantities, then apply the stated changes and compute the new total.

Question 4 of 5

The system of equations

and

has solution

. What is the value of ?

Explanation

Since both equations equal , set them equal to each other: . Then , so .

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.

Question 5 of 5

In the -plane, two lines intersect at the point . Which system of equations could represent these lines?

Explanation

The intersection point of a system is the point that makes both equations true. Substitute into each pair. For , , which is true. For , , which is also true. So this system could represent two lines that intersect at .

Concept summary

For a system of linear equations, the intersection point must satisfy both equations at the same time.

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.

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.

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.

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.

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.

More SAT Math practice