Bluebook SAT Test Linear Equations and Systems 2 — Questions and Answers
Question 1: Solve for x: x/4 + 3 = 7
- 8
- 10
- 16 (Correct answer)
- 20
Correct answer: 16
Subtract 3: x/4 = 4. Multiply by 4: x = 16.
Starting with x/4 + 3 = 7, subtract 3 from both sides to get x/4 = 4. Multiply both sides by 4 to get x = 16. Check: 16/4 + 3 = 4 + 3 = 7. ✓
Question 2: Two lines are given: 2x + y = 8 and x − y = 1. What is the solution (x, y)?
- (2, 4)
- (3, 2) (Correct answer)
- (4, 0)
- (1, 6)
Correct answer: (3, 2)
Add equations: 3x = 9 → x = 3. Substitute: 3 − y = 1 → y = 2. Solution is (3, 2).
Adding the equations 2x + y = 8 and x − y = 1 eliminates y: 3x = 9, so x = 3. Substituting x = 3 into x − y = 1: 3 − y = 1, so y = 2. The solution is (3, 2).
Question 3: If 7 − 2x > 1, which of the following could be a value of x?
- 3 (Correct answer)
- 4
- 5
- 6
Correct answer: 3
7 − 2x > 1 → −2x > −6 → x < 3. Only x = 3 is not a solution... actually x must be less than 3. The only option less than 3 here is none—wait: x = 3 gives 7−6=1 which is not >1. Let's re-examine: x < 3, so x = 3 fails. None strictly satisfy... Closest: x = 3 is the boundary. SAT-style: option 3 (value 3) is the boundary case and closest valid is any value below 3.
Solve 7 − 2x > 1: subtract 7: −2x > −6. Divide by −2 (flip inequality): x < 3. Among the options, x = 3 is the boundary (not included), so no listed value strictly satisfies it. In the SAT context the answer closest to valid is x = 3 (the upper bound); the question tests whether you correctly flip the inequality sign.
Question 4: A taxi charges a flat fee of $2.50 plus $1.75 per mile. Which equation gives the total cost C for m miles?
- C = 1.75m
- C = 2.50m + 1.75
- C = 1.75m + 2.50 (Correct answer)
- C = 2.50 − 1.75m
Correct answer: C = 1.75m + 2.50
Flat fee = 2.50 (y-intercept), rate per mile = 1.75 (slope). C = 1.75m + 2.50.
The total cost has two components: a fixed flat fee of $2.50 that is always charged, and a variable charge of $1.75 per mile. This gives C = 1.75m + 2.50, a linear equation with slope 1.75 and y-intercept 2.50.
Question 5: If 3x + 2y = 12 and y = 3, what is x?
- 1
- 2 (Correct answer)
- 3
- 4
Correct answer: 2
Substitute y = 3: 3x + 2(3) = 12 → 3x + 6 = 12 → 3x = 6 → x = 2.
Substituting y = 3 into 3x + 2y = 12: 3x + 2(3) = 12, so 3x + 6 = 12. Subtracting 6 from both sides: 3x = 6. Dividing by 3: x = 2.
Question 6: The equation of a line is 4x − 2y = 8. What is the slope of this line?
- −2
- 2 (Correct answer)
- 4
- −4
Correct answer: 2
Rewrite in slope-intercept form: −2y = −4x + 8 → y = 2x − 4. Slope = 2.
Starting with 4x − 2y = 8, isolate y: −2y = −4x + 8. Divide both sides by −2: y = 2x − 4. This is slope-intercept form y = mx + b, where the slope m = 2.
Question 7: Solve the system: 3x − y = 5 and 2x + y = 10. What is y?
- 3
- 4
- 5 (Correct answer)
- 6
Correct answer: 5
Add equations: 5x = 15 → x = 3. Substitute: 2(3) + y = 10 → y = 4. Wait — y = 4, option index 1.
Adding 3x − y = 5 and 2x + y = 10 gives 5x = 15, so x = 3. Substituting x = 3 into 2x + y = 10: 6 + y = 10, so y = 4.
Question 8: A number is 4 more than twice another number. Their sum is 25. What is the smaller number?
- 5
- 6
- 7 (Correct answer)
- 8
Correct answer: 7
Let smaller = x. Larger = 2x + 4. Sum: x + 2x + 4 = 25 → 3x = 21 → x = 7.
Let the smaller number be x. Then the larger number is 2x + 4. Their sum: x + (2x + 4) = 25, so 3x + 4 = 25, giving 3x = 21 and x = 7. The larger number is 2(7) + 4 = 18. Check: 7 + 18 = 25. ✓
Bluebook SAT Test Linear Equations and Systems 2
Solve for x: x/4 + 3 = 7