How do you solve the system $x=2y+7$ and $x=y+4$ using substitution?

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Answer 1 · 2017-03-18T00:26:43

$y=-3$ and $x=1$

We know $x=y+4$ Plug that into $x=2y+7$ for x:

$y+4=2y+7$

Move the $y$ to one side by subtracting y on both sides:

$y+4-y=2y+7-y$

$4=y+7$

Subtract 7 on both sides:

$4-7=y+7-7$

$-3=y$

Personally, I like the y on the other side. You are allowed to flip the equation around:

$y=-3$

Now plug this in to one of the equations. I will plug it into the second equation:

$x=-3+4$

$x=1$

Check by plugging in to the other equation:

$1=2(-3)+7$

$1=-6+7$

$1=1$

It works out!

How do you solve the system x=2y+7x=2y+7 and x=y+4x=y+4 using substitution?