How do you solve the system of equations y=-9x-21 and y=5x+7?

Jun 10, 2017

$x = - 2$

Explanation:

Look at the equations:
$y = - 9 x - 21$
and
$y = 5 x + 7$

Because both equations equal (y), they both equal the same.

If an equations says "$y = - 9 x - 21$" , that means we can replace (y) with $- 9 x - 21$.

Therefore when i take the equation: $y = 5 x + 7$ , we can replace (y) to get:
$- 9 x - 21 = 5 x + 7$

Now isolate (x):
$- 9 x - 21 = 5 x + 7 \iff - 21 = 14 x + 7 \iff - 28 = 14 x$
$\iff x = - 2$

Alternatively, you could solve it with graphs. Get a coordinatsystem and look at where the graphs intersect. They will intersect where graph 1 is equal to graph 2, which is essentially the same as what we just did :)