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

Algebra · Systems Of Linear Equations

SAT Systems Of Linear Equations Practice Questions (Free + Explanations) | Quiz 2

Question 12345 of 5

Question 1 of 5

A school store sells notebooks and pens. The table shows one purchase made at the store.The total cost of the purchase was \11\, what is the cost, in dollars, of each notebook?

Explanation Let n be the cost of one notebook. The 2 pens cost a total of 2 (1) = 2 dollars. Since the whole purchase cost 11 dollars, the 3 notebooks cost 11 - 2 = 9 dollars. So each notebook costs 9 \div 3 = 3 dollars. Concept summary Use the total cost and the known cost of one item to find the combined cost of the other item, then divide by its quantity.

Question 2 of 5

A system of equations has the same solution as {x + y = 10 y = 4 Which statement must be true?

Explanation Since y = 4, substitute 4 for y in x + y = 10 . This gives x + 4 = 10, so x = 6 . Therefore, the statement that must be true is x = 6 . Concept summary In a system of equations, use the equation that gives one variable directly and substitute it into the other equation.

Question 3 of 5

A rectangle has a perimeter of 30 units. If the length is 3 units more than the width, what is the width of the rectangle?

Explanation Let the width be w and the length be w + 3 . Since the perimeter of a rectangle is 2 l + 2 w, we have 2 (w + 3) + 2 w = 30. Simplifying gives 4 w + 6 = 30, so 4 w = 24 and w = 6. Therefore, the width is 6 units. Concept summary Use a system or equivalent pair of relationships from a geometric situation: one equation from the perimeter and one from how the side lengths are related.

Question 4 of 5

Tickets for a school play were sold to students and adults. Let s be the number of student tickets sold and a be the number of adult tickets sold. A total of 120 tickets were sold, and there were 30 more student tickets sold than adult tickets. How many adult tickets were sold?

Explanation The two quantities are linked by the conditions s + a = 120 and s = a + 30 . Substitute a + 30 for s in the total: (a + 30) + a = 120. Then 2 a + 30 = 120, so 2 a = 90 and a = 45 . Therefore, the number of adult tickets sold is 45 . Concept summary For a system with a total and a difference, write one equation for the sum and one for how the quantities compare, then substitute to find the unknown.

Question 5 of 5

Line k passes through the point (0, 4) and has slope - 2 . Line m is given by y = - 2 x + 1 . Which system of equations represents lines k and m ?

Explanation A line with slope - 2 and y-intercept 4 has equation y = - 2 x + 4 . Since line m is already given as y = - 2 x + 1, the system is {y = - 2 x + 4 y = - 2 x + 1 Concept summary A line with slope m and y-intercept b can be written as y = m x + b . A point of the form (0, b) gives the y-intercept directly.

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.

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Your results

2of 5 correct

Estimated SAT Math band

600-650

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

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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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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. A school store sells notebooks and pens. The table shows one purchase made at the store. Item Notebooks Pens  Quantity 3 2   The total cost of the purchase was \ 11 . I f e a c h p e n cos t s \ 1 , what is the cost, in dollars, of each notebook?

Q2. A system of equations has the same solution as { x + y = 10 y = 4  Which statement must be true?

Q3. A rectangle has a perimeter of 30 units. If the length is 3 units more than the width, what is the width of the rectangle?

Q4. Tickets for a school play were sold to students and adults. Let s be the number of student tickets sold and a be the number of adult tickets sold. A total of 120 tickets were sold, and there were 30 more student tickets sold than adult tickets. How many adult tickets were sold?

Q5. Line k passes through the point ( 0 , 4 ) and has slope − 2 . Line m is given by y = − 2 x + 1 . Which system of equations represents lines k and m ?