# SOLVING A LINEAR SYSTEM BY ADDING

## About "Solving a linear system by adding"

Solving a linear system by adding :

We can use elimination method to solve a system of linear equations. In this method, one variable 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 adding - 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 adding - Example

Question :

Solve the system of equations by adding. Check your the solution by graphing.

2x - 3y  =  12

x + 3y  =  6

Step 1 :

In the given two equations, the variable y is having the same coefficient (3). And also, the variable y is having different signs.

So we can eliminate the variable y by adding the two equations.

Step 2 :

Solver the resulting equation for the variable x.

3x  =  18

Divide both sides by 3.

3x / 3  =  18 / 3

x  =  6

Step 3 :

Substitute the value of x into one of the equations to find the value of y.

x + 6y  =  6

Subtract 6 from both sides.

aaaaaaaaaaaaaaaaaaaaaa 6 + 3y  =  6 aaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaa  - 6           - 6 aaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaa  -------------- aaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaa          3y  =  0 aaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaa  -------------- aaaaaaaaaaaaaaaaaaa

Divide both sides by 3

3y / 3  =  0 / 3

y  =  0

Step 3 :

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

(6, 0)

Step 4 :

Check the solution by graphing.

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

That is,

y  =  mx + b

2x - 3y  =  12

y  =  (2/3)x - 4

Slope  =  2/3

y-intercept  =  -4

x + 3y  =  6

y  =  -(1/3)x + 2

Slope  =  -1/3

y-intercept  =  2

The point of intersection is (6, 0).

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

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