ACT Question

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ACT Question for December 20th

What is the value of b in the solution to the system of equations below?

A) 17

B) 9

C) 5

D) -3

E) -5

Correct

Incorrect

The correct answer is (D).

Getting to the Answer:The question provides a system of two linear equations with two variables. Since the coefficient of a in the second equation is 1, substitution is a good way to solve for b. Subtract 3b from both sides of a + 3b = -4 to get a = -4 - 3b. Plug this value into the first equation to get 3(-4 - 3b) - 2b = 21. Distribute the 3 to yield -12 - 9b - 2b = 21. Combine like terms to obtain -11b = 33. Divide by -11 to see that b = -3.

(A) Incorrect: this could be the result of incorrectly combining the two equations to get b = 17 instead of 4a + b = 17

(B) Incorrect: this could be the result of calculating that b = 9 rather than -3b = 9

(C) Incorrect: this is the value of a, not b

(D) Correct: this matches the correct calculation

(E) Incorrect: this is the value of -a, not b