Question

Solve the system of linear equations using substitution. Use pencil and paper. Which expression would be easier to substitute into the other equation, in order to solve this problem? Explain your reasoning.

x = 2y - 5
x + 2y = 4

Answer 1

• substitute for x
• (x, y) = (-1/2, 9/4)

Explanation:

When solving a system of equations using substitution, you look for an equation that makes it simple to write an expression for one of the variables in terms of the other(s). Here, the first equation already gives you an expression for x, so it is easiest to substitute for x in the second equation:

(2y -5) +2y = 4 . . . . . . (2y-5) substituted for x

4y = 9 . . . . . . . . . . add 5 and simplify

y = 9/4 . . . . . . . . divide by 4

x = 2(9/4) -5 = 9/2 -10/2 = -1/2

The solution is (x, y) = (-1/2, 9/4).