Question

Consider the following pair of equations:

y = −2x + 8
y = x − 1



Explain how you will solve the pair of equations by substitution. Show all your work and write the solution in (x, y) form.

Answer 1

To solve the pair of equations by substitution, we first isolate one of the variables in one of the equations and then substitute it into the second equation.

Given equations:
y = -2x + 8 (Equation 1)
y = x - 1 (Equation 2)

From Equation 1, we can rewrite it as:
y = -2x + 8

Now, we substitute this expression for y into Equation 2:
-2x + 8 = x - 1

Now, solve for x:
-2x - x = -1 - 8
-3x = -9
x = 3

Now that we have found that x = 3, we can substitute this back into Equation 2 to find y:
y = 3 - 1
y = 2

Therefore, the solution to the pair of equations is (x, y) = (3, 2).