SAT Math
Linear Equations in Two Variables
Linear Equations in Two Variables is a skill in the Algebra domain of the Digital SAT Math section. These are practice questions on it, and each answer choice comes with an explanation of why it is right or wrong.
11 questions. After every answer you’ll see why each choice is right or wrong, not just the one you picked.
Sample questions
Open a question to see the answer choices and the correct answer.
A bakery sells small and large loaves of bread. In one day, the bakery's sales totaled $612.50. The equation 3.25x + 5.50y = 612.50 represents this situation, where x is the number of small loaves sold and y is the number of large loaves sold. According to the equation, which of the following represents the total revenue, in dollars, from small loaves sold that day?
- A. 3.25x ✓
- B. 5.50y
- C. 3.25
- D. 3.25 + x
Correct answer: A. In the equation, 3.25 is the price per small loaf and x is the number sold, so the product 3.25x is the total revenue from small loaves specifically.
Line k is defined by the equation y = −(2/5)x + 9. Line j is perpendicular to line k in the xy-plane. What is the slope of line j?
- A. −2/5
- B. 5/2 ✓
- C. 2/5
- D. −5/2
Correct answer: B. Perpendicular lines have slopes that are negative reciprocals of each other; the negative reciprocal of −2/5 is 5/2.
A moving company charges a flat fee plus an hourly rate. The total cost C, in dollars, of a move that takes h hours is given by the equation C = 45h + 120. What does the number 120 most likely represent in this context?
- A. The hourly rate charged for each hour of the move.
- B. The total cost of a move that takes exactly one hour.
- C. The flat fee charged regardless of how many hours the move takes. ✓
- D. The number of hours it takes to complete an average move.
Correct answer: C. 120 is the constant term in the equation, added regardless of the value of h, so it represents a flat fee charged no matter how long the move takes.
Line k is defined by y = −(3/4)x + 2. Line j is perpendicular to line k. What is the slope of line j?
- A. 4/3 ✓
- B. −4/3
- C. −3/4
- D. 3/4
Correct answer: A. Correct — the slope of a perpendicular line is the negative reciprocal of the original slope; the negative reciprocal of −3/4 is 4/3.
A company's monthly cost model is C = 1,200 + 35n, where n is the number of units produced and C is the total cost in dollars. What does the value 1,200 represent in this context?
- A. the cost of producing one additional unit
- B. the company's fixed monthly cost, incurred even if zero units are produced ✓
- C. the total cost of producing 1,200 units
- D. the maximum number of units the company can produce in a month
Correct answer: B. Correct — since 1,200 is added regardless of n, it represents a fixed cost that does not depend on how many units are produced.