How do you solve the system of equations algebraically $7x+y=9, 5x-y=15$ ?

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Answer 1 · 2016-12-16T03:04:15

$(x,y)=(2,-5)$

We can add the two equations together to eliminate the $y$ term, solve for $x$ , then substitute in. Like this:

$7x+y=9$
$5x-y=15$

$12xcolor(white)(000)=24$

$x=2$

Substituting into either of the original equations will give us $y$ (I'll do both to show it doesn't matter):

$7x+y=9$

$7(2)+y=9$

$14+y=9$

$y=-5$

~~~~~

$5x-y=15$

$5(2)-y=15$

$10-y=15$

$-y=5$

$y=-5$

How do you solve the system of equations algebraically 7x+y=9, 5x-y=157x+y=9, 5x-y=15?