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

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

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

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

Answer 1

The system is
x + y = 5
7x + 8y = 37

A is valid: multiply the first by −7 gives −7x −7y = −35; adding to 7x + 8y = 37 yields y = 2, which eliminates x.

B, C, and D are not appropriate elimination steps because they do not produce opposite coefficients to cancel a variable (they give fractional or mismatched coefficients), so adding would not eliminate either variable.

Thus only A is a valid first step. (Solving further: y = 2, then x = 3.)