Question

A system of equations is shown below.

{
x
+
y
=
5
7
x
+
8
y
=
37

Which of the following are valid first steps in an algebraic method to solve the system of equations?

A.
Divide the first equation by –7 and then add the two equations.

B.
Divide the first equation by 56 and then add the two equations.

C.
Multiply the first equation by 56 and then add the two equations.

D.
Multiply the first equation by –7 and then add the two equations.

Answer 1

D.

Multiply the first equation by −7: −7x − 7y = −35. Add this to 7x + 8y = 37 to eliminate x:
y = 2. Then x + 2 = 5 so x = 3.