Solve the system of linear equations using the Gauss-Jordan elimination method x – 2y = 8 3x + 4y = 4

Question

 Solve the system of linear equations using the Gauss-Jordan elimination method 

 

x – 2y = 8

3x + 4y = 4

Answer 1

 x  - 2y = 8
3x + 4y = 4

 

Multiply the first equation by 2:

 

2*( x - 2y = 8)

2x - 4y = 16

 

Now add the modified first equation to the second equation to eliminate the y-terms:

 

2x - 4y = 16

3x + 4y =  4

--------------

5x +  0  = 20

 

5x = 20

x = 4

 

To find y, plug x = 4 into either original equation and solve for y:

 

x - 2y = 8

x - 8 = 2y

x/2 - 4 = y

4/2 - 4 = y

2 - 4 = y

-2 = y

 

Check the answer by plugging x = 4, y = -2 into both original equations

x - 2y = 8

4 - 2(-2) = 8

4 + 4 = 8

8 = 8

 

3x + 4y = 4

3(4) + 4(-2) = 4

12 - 8 = 4

4 = 4

 

It checks!