Solve the system of equations

Question

Solve the system of equations

 

x-2y+3z = 13

2x+y+z = 1

-3x+2y-2z = -13

Answer 1

Add equations 1 and 3 together to eliminate the y-variable.

x - 2y + 3z = 13

-3x +2y -2z =-13

the result is:  -2x +z =0 (equation 4)

 

Then multiply the second equation with 2 and add to equation 1

x - 2y +3z = 13

4x + 2y + 2z = 2 (this is the result of multiplying equation 2 with '2')

Adding these gives us: 5x+5z = 15 OR x+z = 3 (equation 5)

 

Now use these two equations with 2-variable to eliminate another variable.

Subtracting equation 5 from equation 4:

-2x+z =0

-x -z = -3 (equation 5 is multiplied by a '-1')

 

So, we get -3x=-3 --> x=1

 

Substitute x=1 into equation 5 to get z=2

 

Now, substitute x=1 and z=2 into equation 1

 

1-2y+3(2)=13

-2y+7=13

-2y=6

y=-3

 

SOLUTION (1,-3,2)