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?

Answer 1

Valid first steps include either substitution or elimination. Examples:

- Substitution: solve x + y = 5 for x (or y), e.g. x = 5 − y, then substitute into 7x + 8y = 37 to get 7(5 − y) + 8y = 37.

- Elimination by multiplying the first equation so one variable cancels. For example:
- Multiply x + y = 5 by 7 to get 7x + 7y = 35 and subtract from 7x + 8y = 37 to get y = 2, then x = 3.
- Or multiply x + y = 5 by 8 to get 8x + 8y = 40 and subtract 7x + 8y = 37 to get x = 3, then y = 2.

All of these are valid first steps. The solution is x = 3, y = 2.