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 the two equations of the system to obtain single equation in one variable.

The following steps will be useful to solve a system of linear equations by adding.

Step 1 :

The variable which is eliminated must have the same coefficient in both the equations. If not, make them to be same using least common multiple and multiplication.

Step 2 : 

The variable which is eliminated must have different signs. If not, multiply one of the equations by negative sign. 

Step 3 :

Now add the two equations to eliminate one of the variables and solve for the other variable. 

Step 4 :

Substitute the value of the variable received in step 3 into one of the equations to find the value of the eliminated variable. 

Question :

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

2x - 3y  =  12

x + 3y  =  6

Answer :

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 

The point of intersection is (6, 0).

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