Question

Solve by using substitution
-4x+y=6   and   -5x-y=21

Answer 1

`\left \{ {{-4x+y=6} \atop {-5x-y=21}} \right. \\\\ \left \{ {{y=6+4x} \atop {-5x-y=21}} \right. \\\\Substitute\ first\ equation\ into\ the\ second\\\\ -5x-(6+4x)=21\\ -5x-6-4x=21\\ -9x-6=21\ \ \ |add\ 6\\\\ -9x=27\ \ \ |divide\ by\ -9\\\\ x=-3\\ y=6+4*(-3)=6-12=-6\\\\ \left \{ {{y=-6} \atop {x=-3}} \right.`

Answer 2

So if you're solving by substitution, one equation must be in slope intercept form. Ill just go with the first one.

-4x+y=6
+4x +4x
y=6+4x

Now substitute the value of y in for the value of y in the second equation:
-5x-(6+4x)=21
-5x-6-4x=21
-9x-6=21
+6 +6
-9x=27
-9 -9

x=-3

Now input that into the first equation:
-4(-3)+y=6
12+y=6
-12 -12
y=-6


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