Question

How can I solve this problem using substitution, please show the work. (x,y)

y=x+8

x+y=2

Answer 1

Answer: Y= 10

Y= X+8 X+Y=2
-x -x
Y= -x+2
Y=x+8
Y=-x+2
Y=10

Answer 2

(-3,5)

Explanation:

To solve using substitution, first isolate one variable in one of the given equations. Then, substitute the value you received from that equation for the matching variable in the second equation. Finally, substitute that value back into any of the equations to have both the x and y values.

1) The y in y = x + 8 is already isolated, so let's substitute that value for the y in x + y = 2. Substitute x + 8 for y in x + y = 2, then solve:

`x + y = 2\\x + (x + 8) = 2 \\x + x + 8 = 2\\2x + 8 = 2 \\2x = -6\\x =-3\\`

Therefore, the x-value of the solution is -3.

2) Substitute the x value back into any of the one equations to find the value. Any choice is fine - in my work, I chose to substitute -3 for the x in y = x + 8:

`y = x + 8 \\y = (-3) + 8\\y = -3 + 8\\y = 5`

Therefore, the y-value of the solution is 5.

3) Thus, the solution is (-3, 5).