Bluebook SAT Test Linear Equations and Systems

Question 1

If 3x + 7 = 22, what is the value of x?

Accepted Answer

5

Answer

Subtract 7 from both sides: 3x = 15. Divide by 3: x = 5.

Question 2

A system of equations is given: y = 2x + 1 and y = -x + 7. What is the value of x at the solution?

Accepted Answer

2

Answer

Set equal: 2x + 1 = -x + 7 → 3x = 6 → x = 2.

Question 3

The sum of two consecutive integers is 47. What is the larger integer?

Accepted Answer

24

Answer

Let the integers be n and n+1. n + (n+1) = 47 → 2n + 1 = 47 → n = 23. The larger is 24.

Question 4

If 5(x − 2) = 3x + 6, what is x?

Accepted Answer

8

Answer

Expand: 5x − 10 = 3x + 6. Subtract 3x: 2x − 10 = 6. Add 10: 2x = 16. Divide: 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?

Accepted Answer

4

Answer

Let n = notebooks, p = pens. n + p = 9 and 3n + p = 17. Subtracting: 2n = 8 → n = 4.

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