MCQsLearnSAT

Algebra · Systems Of Linear Equations

SAT Systems Of Linear Equations Practice Questions (Free + Explanations) | Quiz 5

Question 12345 of 5

Question 1 of 5

A concert venue sold tickets in advance for two seating sections: standard and premium. On one day, the venue sold tickets total and collected \4{,}560\ more than a standard ticket. If a standard ticket cost \30

Explanation

Since a standard ticket cost \30\. Let be the number of standard tickets and be the number of premium tickets. Then

and

Substitute into the revenue equation:

Simplify:

So, premium tickets were sold.

Concept summary

Model the situation with a system: one equation for the total number of items and one for the total cost. Then solve for the requested quantity.

Question 2 of 5

For the system of equations

the solution is . What is the value of ?

Explanation

Substitute into the first equation to find :

So . Now use the second equation with and :

Therefore,

Concept summary

When a system's solution is given as an ordered pair containing variables, substitute the known coordinate values into each equation to find the unknown parameters, then evaluate the requested expression.

Question 3 of 5

For the system of equations

what equivalent equation in can be obtained by substituting the expression for from the first equation into the second equation?

Explanation

From the first equation, . Substitute that entire expression for into the second equation :

The parentheses are necessary because the entire expression is replacing . So the equivalent equation in is .

Concept summary

When substituting one equation into another in a system, replace the variable with the entire equivalent expression and use parentheses when needed.

Question 4 of 5

In the -plane, the graphs of and intersect at point . What is the -coordinate of point ?

Explanation

At the intersection, both equations are true for the same point. Rewrite as . Then set the two expressions for equal:

Add to both sides and add to both sides:

So . Substitute into either equation:

Therefore, the -coordinate of point is .

Concept summary

For the intersection of two lines, the coordinates satisfy both equations at the same time. Set the expressions equal or substitute to find the shared point.

Question 5 of 5

A school club sells notebooks and pens at a fundraiser. Each notebook costs \3\. On one day, the club sold a total of items for a total of \43

Explanation

Let be the number of notebooks and be the number of pens. The total number of items gives . The total money gives . Substitute into the second equation:

So the club sold notebooks.

Concept summary

Represent each quantity with a variable, write one equation for the total number of items and another for the total cost, then solve the system.

Your results

0of 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

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