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

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Answer 1 · 2017-01-17T09:17:30

$x = 5$ $x=5$ and $y = 7$ $y=7$

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

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

$x + y = 12$ $x+y=12$

Subtract $x$ $x$ from both sides.

$y = 12 - x$ $y=12-x$

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

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

$3 x - 2 y = 1$ $3x-2y=1$

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

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

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

$3 x - 24 + 2 x = 1$ $3x-24+2x=1$

$5 x - 24 = 1$ $5x-24=1$

Add $24$ $24$ to both sides.

$5 x = 25$ $5x=25$

Divide both sides by $5$ $5$ .

$x = 5$ $x=5$

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

$x + y = 12$ $x+y=12$

$5 + y = 12$ $color(blue)5+y=12$

Subtract $5$ $5$ from each side.

$y = 7$ $y=7$

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