SOLVING A LINEAR SYSTEM BY SUBTRACTING

About "Solving a linear system by subtracting"

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.

Solving a linear system by subtracting : Steps

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

Solving a linear system by subtracting - Example

Question :

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

3x + 3y  =  6

3x - y  =  - 6

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

(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). After having gone through the stuff given above, we hope that the students would have understood "How to solve a linear system by subtraction".

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