# Substitution stepsShow the steps followed when solving systems of linear equations x-y=3; 2x+y=12

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Given the system:

x-y=3.............(1)

We have a system of two equations and two variables.

We can use the elimination and substitution method to solve.

We will add (1) and (2).

==> 3x = 15

Now we will divide by 3 both sides.

==> x = 15/3 = 5

==> x = 5

Now we will substitute x=5 into one of the equations to find y.

We will substitute into equation (1).

x - y = 3

==> 5-y = 3

==> y = 2

**Then, the solution to the system is the pair ( 5, 2)**

x - y = 3

Therefore

- y = 3 - x Multiply both sides by -1

y = -3 + x

Substitute this in to the other equation.

2x + -3 + x = 12 Add the x terms

3x + -3 = 12 Add 3 to both sides

3x = 15 Divide both sides by 3

x = 5

Substitute back to the first equation

5 - y = 3 Subtract 5 from both sides

-y = -2 Multiply both sides by -1

y = 2

The steps are the followings:

1) We'll change the first equation into:

x = 3 + y

2) We'll substitute the first changed equation into:

2(3 + y) + y = 12

3)We'll remove the brackets:

6 + 2y + y = 12

4) We'll move the number alone from the left to the right side:

2y + y = 12 - 6

5)We'll combine like terms:

3y = 6

6)We'll divide by 3:

y = 2

7)We'll return into the 1st changed equation:

x = 3 + 2

x = 5

**The solution of the system is the pair (5;2).**