Bluebook SAT Test Linear Equations and Systems 1 — Questions and Answers
Question 1: If 3x + 7 = 22, what is the value of x?
- 3
- 5 (Correct answer)
- 7
- 9
Correct answer: 5
Subtract 7 from both sides: 3x = 15. Divide by 3: x = 5.
To solve 3x + 7 = 22, first subtract 7 from both sides to get 3x = 15. Then divide both sides by 3 to find x = 5. Substituting back: 3(5) + 7 = 15 + 7 = 22. ✓
Question 2: A system of equations is given: y = 2x + 1 and y = -x + 7. What is the value of x at the solution?
- 1
- 2 (Correct answer)
- 3
- 4
Correct answer: 2
Set equal: 2x + 1 = -x + 7 → 3x = 6 → x = 2.
Since both expressions equal y, set 2x + 1 = -x + 7. Add x to both sides: 3x + 1 = 7. Subtract 1: 3x = 6. Divide by 3: x = 2. Then y = 2(2) + 1 = 5.
Question 3: The sum of two consecutive integers is 47. What is the larger integer?
- 22
- 23
- 24 (Correct answer)
- 25
Correct answer: 24
Let the integers be n and n+1. n + (n+1) = 47 → 2n + 1 = 47 → n = 23. The larger is 24.
Let the two consecutive integers be n and n+1. Their sum equals 47: n + (n+1) = 47, so 2n + 1 = 47, giving 2n = 46 and n = 23. The larger integer is n+1 = 24.
Question 4: If 5(x − 2) = 3x + 6, what is x?
- 4
- 6
- 8 (Correct answer)
- 10
Correct answer: 8
Expand: 5x − 10 = 3x + 6. Subtract 3x: 2x − 10 = 6. Add 10: 2x = 16. Divide: x = 8.
Distribute 5 on the left side: 5x − 10 = 3x + 6. Subtract 3x from both sides: 2x − 10 = 6. Add 10 to both sides: 2x = 16. Divide by 2: x = 8.
Question 5: A store sells notebooks for $3 each and pens for $1 each. Maria spends $17 and buys 9 items total. How many notebooks did she buy?
- 3
- 4 (Correct answer)
- 5
- 6
Correct answer: 4
Let n = notebooks, p = pens. n + p = 9 and 3n + p = 17. Subtracting: 2n = 8 → n = 4.
Let n = number of notebooks and p = number of pens. System: n + p = 9 and 3n + p = 17. Subtract the first from the second: 2n = 8, so n = 4. Then p = 9 − 4 = 5. Check: 3(4) + 1(5) = 12 + 5 = 17. ✓
Question 6: Which value of x satisfies 2(3x + 4) = 5x + 15?
- 5
- 6
- 7 (Correct answer)
- 8
Correct answer: 7
Expand: 6x + 8 = 5x + 15. Subtract 5x: x + 8 = 15. Subtract 8: x = 7.
Distributing on the left: 6x + 8 = 5x + 15. Subtract 5x from both sides: x + 8 = 15. Subtract 8: x = 7. Verification: 2(3·7 + 4) = 2(25) = 50; 5(7) + 15 = 50. ✓
Question 7: If 4x − 3y = 10 and x = 4, what is the value of y?
- 1
- 2 (Correct answer)
- 3
- 4
Correct answer: 2
Substitute x = 4: 4(4) − 3y = 10 → 16 − 3y = 10 → 3y = 6 → y = 2.
Plug x = 4 into 4x − 3y = 10: 4(4) − 3y = 10, so 16 − 3y = 10. Subtract 16 from both sides: −3y = −6. Divide by −3: y = 2.
Question 8: A linear equation has slope 3 and passes through (0, −5). Which equation represents this line?
- y = −5x + 3
- y = 3x − 5 (Correct answer)
- y = 3x + 5
- y = 5x − 3
Correct answer: y = 3x − 5
Slope-intercept form: y = mx + b. m = 3, b = −5 (y-intercept at (0,−5)). So y = 3x − 5.
The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept. Given m = 3 and the line passes through (0, −5), the y-intercept b = −5. The equation is y = 3x − 5.
Bluebook SAT Test Linear Equations and Systems 1
If 3x + 7 = 22, what is the value of x?