Question

Substitution Method: x+y (1)
2x-y=2 (2)
Find x and y.

Answer 1

Answer is x= 2 2/3 y = 3 1/3
Or fractions (8/3, 10/3)

Step by step

Substitution method means to substitute the value of one equation into the other and solve

We have

EQ 1) x + y = 6 or x = 6 - y
EQ 2) 2x - y = 2

I changed EQ 1 so the x variable is on one side for easy substitution

Substitute EQ 1 in for x in EQ 2

2(6-y) -y = 2
Distribute multiply

12 - 2y -y = 2
Combine like terms

12 -3y = 2
Subtract 12 from both sides to isolate y

12 - 12 -3y = 2 - 12
Combine

-3y = -10
Divide both sides by -3 to solve

y = 10/3 or 3 1/3

Now we substitute value of y into EQ 1 to find x

x + 3 1/3 = 6
Subtract 10/3 from both sides to solve x

x + 3 1/3 - 3 1/3 = 6 - 3 1/3

x = 2 2/3

Now we check our work

Substitute x and y into EQ 1

2 2/3 + 3 1/3 = 6

6 = 6

They equal so the solution is correct!

Answer 2

x = 8/3

y = 10/3

Explanation:

We add (1) and (2) to get 3x = 8. This means that x = 8/3. We substitute it back into (1) to get 8/3 + y = 6 which shows that y = 10/3