Question

1. What is the solution to the system of equations? Use the substitution method to solve the system of equations. Show all of your work!

y = x + 5
4x − 4y = −20

Answer 1

There are infinite solutions to this problem

Explanation:

The equations are scale multiples of each other...

Take the first equation and subtract x from both sides...

y = x + 5 becomes

-x + y = 5

Now divide the equation by -1...

x - y = -5

Now multiply the equation by 4....

4x - 4y = -20

This is now the same as equation 2. The lines lay on top of each other, so there are infinite points (x, y) that will solve this equation, what ever value 'x' is, 'y' will be 5 values higher

(0, 5)

(1, 6)

(5, 10)

Are some examples

Answer 2

The two equations are identical, thus there are infinite number of solutions

Explanation: