Question

Use the substitution method to solve the given system of equations. Write your answer as an ordered pair, (x, y).

Answer 1

(-3, -2)

Explanation:

Look at the second equation, we can easily rearrange it to make x the subject.

x - 4y = 5

x = 4y + 5

Now lets put that into the second equation

2x - 2y = -2

2(4y + 5) - 2y = -2

6y + 10 = -2

6y = -12

y = -2

Now lets find x!

x = 4y + 5

x = 4(-2) + 5

x = -3

Now lets format the answer like the question says (ordered pair)

(-3, -2)

Recap: We used substitution and made an equation to work out one of the variables first, then found the second variable using the first.

Answer 2

2x - 2y = -2

x - 4y = 5

In x -4y =5, add 4y to both sides to get x = 4y +5

Now substitute that equation for x in the first equation:

2x - 2y = -2

2(4y +5) - 2y = -2

Simplify:

8y +10 - 2y = -2

Combine like terms:

6y +10 = -2

Subtract 10 from both sides:

6y = -12

Divide both sides by 6:

y = -12 /6

y = -2

Now you have y, substitute y in the second equation to solve for x:

x - 4y = 5

x -4(-2) = 5

Simplify:

x+8 = 5

Subtract 8 from both sides:

x = -3

Now you have x = -3 and y = -2

The answer is (-3,-2)