Question

Consider the following pair of equations:

y = x + 4
y = −2x − 2

Explain how you will solve the pair of equations by substitution. Show all the steps and write the solution in (x, y) form. (5 points)

Answer 1

To solve the pair of equations by substitution, we will first rearrange the first equation to solve for x:

y = x + 4
x = y - 4

Then we substitute x = y - 4 into the second equation:

y = -2(y - 4) - 2
y = -2y + 8 - 2
y = -2y + 6
3y = 6
y = 2

Now that we have found the value of y, we can substitute it back into the first equation to solve for x:

x = 2 - 4
x = -2

Therefore, the solution to the pair of equations is (-2, 2).