How do you solve the system of equations: -3x-3y=3 and y=-5x-17?

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Answer 1 · 2018-04-24T21:43:37

When solved by substitution:

$x= -4$
$y= 3$

Let

$-3x - 3y = 3$

be eqn $(1)$ and let

$y = -5x -17$

be eqn $(2)$ . By means of substitution, we substitute eqn $(2)$ into eqn $(1)$ to find the unknown, $x$ .

We arrive at:

$-3x -3(-5x - 17) = 3$

$-3x + 15x + 51 = 3$

$15x - 3x = 3 - 51$

$12x = -48$

$x = (-48)/12$

$x = -4$

We now have the value of $x$ , hence we can substitute $x=-4$ in eqn $(2)$ to find the unknown $y$ . By doing this, we arrive at:

$y = -5(-4) - 17$

$y = 20 - 17$

$y = 3$

Hence $x= -4 and y= 3$ .

But to be sure, always double-check your work by replacing your values in the equations to see if they make the equations true.

$-3(-4) - 3(3) =3$
$12 - 9 = 3 ->$ true

$3 = -5(-4) - 17$
$3 = 20 - 17 ->$ true

The values of $x$ and $y$ make the equations true, hence $x=-4$ and $y=3$ .