Consider the following pair of equations:

Question

y = −2x + 8
y = x − 1

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

Answer 1

To solve the pair of equations by substitution, we can set the two expressions for y equal to each other and then solve for x.

-2x + 8 = x - 1
-2x - x = -1 - 8
-3x = -9
x = 3

Now that we have found the value of x, we can substitute it back into one of the original equations to find the value of y. Let's use the first equation y = -2x + 8:

y = -2(3) + 8
y = -6 + 8
y = 2

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