Math CentralQuandaries & Queries


Question from Nicolette, a student:

I am working on linear programming problems that I need to solve pairs of linear equations for. I am confused and am not sure how to solve these problems!
5x+3y=7 y=x-3 How can i solve this using the substitution method?

Hi Nicolette,

Your equations are set up nicely to use the substitution method.

5x + 3y = 7                 (1)

y = x - 3                      (2)

Equation 2 tells you that y is x - 3 so you can substitute x - 3 for y in the first equation.

5x + 3(x - 3) = 7

Simplification gives me

5x + 3x - 9 = 7.

Solve this equation for x and then substitute the value of x into equation (2) to find y. Once you have values of x and y you can substitute them into equation (1) to verify your answer.

I hope this helps,

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