Question

Solve the system by substitution. Then check the solution again in each equation.

y =-2x - 6
y = x + 15

Answer 1

x=−2y=2

Explanation:

Take the value of x from the first equation:x=2−2y (1)and substitute for x into the second:y=2(2−2y)+6

solve for y ;y=4−4y+6y=105=2

Substitute back into

(1) and find :x=2−4=−2

Answer 2

y - -2x - 6 (1)
y = x+15 (2)

From (2) we get x = y-15
We put that in (1) and we get -2(y-15)-6 = y
-2y+30-6 = y
-2y+24=y
-2y+24-y=0
-3y+24 = 0 ==> -3y = -24 ==> y = 8

We put that value in (2) and we get x = 8-15 = -7

Now in order to verify this, we replace the variables and see if (1) = (2)

y = -2x - 6 ==> (-2 * -7) - 6 = 14-6 = 8 (1')
y = x + 15 = -7 + 15 = 8 (2')

(1') = (2') ==> the solution is x = -7 and y = 8