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Solving the system of equations by the substitution method?

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2 Answers

The way I like to do substitution is by learning the "y" variable first.  This means one of the equations must be set to "y=".  The second question looks like it will have nicer numbers after isolating "y".

Move y to one side ---> -8y=-4x + 12

Isolate y by dividing -8 from both sides --> y=(1/2)x - 12

Now, you can replace the y in the first equation, 7y=x+2 with (1/2)x - 12 and solve for x.  From there, you can then finally solve for y by using the number you got for x by substitution.

7y= x + 2 Solve for x Subtract 2 from both sides 7y - 2 = x Plug this equation into the next one using 7y - 2 for x 4x - 8y = 12 4(7y - 2) - 8y = 12 28y - 8 - 8y = 12 20y - 8 = 12 20y = 20 y = 1 Now plug 1 into y in either equation to solve for x 7y - 2 = x 7 - 2 = x x=5