Question

If (r, s) is the solution to the system of equations, what is the value of r? −8r − 8s = 100 r − 2s = 10

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve this system of equations, we can use the method of substitution.

First, let's solve the second equation for r:
r - 2s = 10
r = 10 + 2s

Now we can substitute this expression for r into the first equation:
-8r - 8s = 100
-8(10 + 2s) - 8s = 100
-80 - 16s - 8s = 100
-80 - 24s = 100

Add 80 to both sides of the equation:
-24s = 180

Divide both sides of the equation by -24:
s = -180/24
s = -15/2

Now, substitute this value for s back into the equation for r:
r = 10 + 2s
r = 10 + 2(-15/2)
r = 10 - 15
r = -5

Therefore, the value of r is -5.