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.
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).