How do you solve $3x+6y=-6$ and $-7x+y=29$ using substitution?

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Answer 1 · 2018-04-01T18:57:24

$(x,y)=(-4,1)$

Solve one of these equations for $y$ to make substitution possible. The second equation appears best suited for this:

$-7x+y=29$

$y=7x+29$

We can now replace all instances of $y$ in the first equation with $7x+29:$

$3x+6(7x+29)=-6$

$3x+42x+174=-6$

$45x=-6-174$

$45x=-180$

$x=-180/45$

$x=-4$

To find $y,$ plug in the result above into either of the two equations. We solved the second one for $y,$ so that will be the easiest one to use:

$y=7(-4)+29$

$y=1$

How do you solve 3x+6y=-63x+6y=-6 and -7x+y=29-7x+y=29 using substitution?