Math: e2e3942f

ID: e2e3942f

(SAT Suite Question Bank > Find Questions > Assessment: SAT + Test: Math + Domain: Algebra)

Comment: Match those coefficients.

Method 1: Like question 466b87e3, this question can be answered on sight within a few seconds, since both equations in the system start with y =. Simply put, if the coefficients match for both x and y terms, you will be dealing with a system of equations that either has no solution or an infinite number of solutions. In this case, if a = 2, the system will have no solution, since it is impossible for y to equal 2x + 1 and 2x + 8 simultaneously. The correct answer is (D).

Method 2: Plug in the equations to Desmos and use a slider for a. When the two lines are parallel, you will have the correct answer.

As you can see, the lines are parallel (no solution) when a = 2, so the correct answer is (D).

Method 3: You could use substitution or elimination to work the problem algebraically, or you could test the answer choices themselves if you were at a loss. Either method would require an understanding of how systems of equations work. I will illustrate how to solve using substitution.

y = 2x + 1

y = ax - 8

(2x + 1) = ax - 8

2x - ax = -9

The only way to guarantee that no matter what value x may be, other than 0, the ax term will not lead to a difference of -9 is if a = 2, since 2x - 2x = 0. Thus, a = 2, and the correct answer is (D).