**Solving a linear system by subtracting :**

The elimination method can be used to solve a system of linear equations. In this method, one of the variables is eliminated by adding or subtracting the two equations of the system to obtain a single equation in one variable.

**Step 1 :**

Add or subtract the equations to eliminate one of the variables.

**Step 2 :**

Solve the resulting equation for the other variable.

**Step 3 :**

Substitute the value of the variable received in step 2 into one of the equations to find the value of the variable eliminated in step 1

**Question :**

Solve the system of equations by subtracting. Check the solution by graphing.

3x + 3y = 6

3x - y = - 6

**Answer :**

**Step 1 : **

In the given two equations, the variable x is having the same coefficient (3), And also, the variable x is having the same sign in both the equations.

So we can eliminate the variable x by subtracting the two equations.

(3x + 3y) - (3x - y) = (6) - (-6)

3x + 3y - 3x + y = 6 + 6

Simplify.

4y = 12

Divide both sides by 4.

4y / 4 = 12 / 4

y = 3

**Step 2 : **

Plug y = 3 in one of the equations.

3x - y = - 6

3x - 3 = - 6

Add 3 to both sides.

(3x - 3) + 3 = (-6) + 3

3x - 3 + 3 = -6 + 3

Simplify.

3x = -3

Divide both sides by 3

3x / 3 = -3 / 3

x = - 1

**Step 3 : **

Write the solution as ordered pair as (x, y).

(-1, 3)

**Step 4 : **

Check the solution by graphing.

To graph the equations, write them in slope-intercept form.

That is,

y = mx + b

3x + 3y = 6

y = - x + 2

Slope = - 1

y-intercept = 2

3x - y = - 6

y = 3x + 6

Slope = 3

y-intercept = 6

The point of intersection is (-1, 3).

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