How do solve the following linear system?: $9 x-6y =3 , x + y= 12$ ?

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Answer 1 · 2017-01-17T09:17:30

$x=5$ and $y=7$

$9x-6y=3$
$x+y=12$

Using the second equation, determine a value for $y$ .

$x+y=12$

Subtract $x$ from both sides.

$y=12-x$

Reduce the first equation by dividing all terms by $3$ .

$9x-6y=3$

$3x-2y=1$

Substitute $y$ with $color(red)((12-x))$ .

$3x-2color(red)((12-x))=1$

Open the brackets and simplify. The product of two negatives is a positive.

$3x-24+2x=1$

$5x-24=1$

Add $24$ to both sides.

$5x=25$

Divide both sides by $5$ .

$x=5$

In the second equation, substitute $x$ with $color(blue)5$ .

$x+y=12$

$color(blue)5+y=12$

Subtract $5$ from each side.

$y=7$

How do solve the following linear system?: 9 x-6y =3 , x + y= 12 9 x-6y =3 , x + y= 12 ?