Question

Next, we need to make the coefficients of the x variables opposites (as in 5 and -5, etc.), since we want to eliminate the x's. To do this, we will find a common multiple (here, the lowest common multiple is 20). Then, we will multiply every term by the number that makes the coefficient of x our common multiple. We will make the first equation with a coefficient of 20 for the x and the second with a coefficient of -20 for the x. See this visually below. 5x − 2y = 10 ➜ 4(5x) − 4(2y) = 4(10) ➜ 20x - 8y = 40 4x − 3y = 15 ➜ -5(4x) − -5(3y) = -5(15) ➜ -20x + 15y = -75 Lastly, add these two equations together. The x's are eliminated. This also will let us solve for y. 20x - 8y = 40 -20x + 15y = -75 -------------------------------- 7y = -35 y = -5

A. y = -5
B. y = 5
C. y = 10
D. y = -10

Answer 1

By multiplying the original equations to obtain coefficients of 20 and -20 for x, the student successfully eliminates the x variable when the new equations are added together, solving for y to find that y = -5. Answer A, y = -5, is correct.

Step-by-step explanation:

The goal is to solve a system of linear equations by elimination. The student seeks to get opposites coefficients for the variable x in the two equations so they cancel each other out when added together, thereby eliminating the variable x. After finding the least common multiple of the coefficients of x (which is 20), the student multiplies each equation by an appropriate factor to get coefficients of 20 and -20 for the variable x, respectively.

When the two new equations, 20x - 8y = 40 and -20x + 15y = -75, are added together, the x variables cancel out, resulting in a new equation, 7y = -35. Upon dividing both sides by 7, we find that y = -5, which corresponds to answer choice A. Therefore, A. y = -5 is the correct answer to the student's question.