Question

The equations –a – 7b = 14 and –4a – 14b = 28 represent a system of linear equations. Which statement correctly explains how to eliminate the variable b when solving the system of equations?
Multiply the first equation by –2 and add it to the second equation. Then solve the resulting equation, –2a = 0.
Multiply the first equation by 2 and add it to the second equation. Then solve the resulting equation, –2a = 0.
Divide the second equation by –4 and add it to the first equation.
Divide the second equation by 4 and add it to the first equation.

Answer 1

Multiply the first equation by –2 and add it to the second equation.

Reason: (–a – 7b = 14)×(–2) → 2a + 14b = –28.
Add to (–4a – 14b = 28): (2a − 4a) + (14b − 14b) = −2a and (−28 + 28) = 0, so −2a = 0 → a = 0.
Then −a − 7b = 14 gives −0 − 7b = 14, so b = −2.