Solve the system

Question

Solve the system.

5x + 6z = 4y − 48
9x + 2y = 3z − 68
3x + y = −31

Answer 1

5x + 6z = 4y − 48
9x + 2y = 3z − 68
3x + y = −31

 

Let's try rewriting them a bit:

5x + 6z - 4y = -48
9x + 2y - 3z = -68
y = -3x - 31

 

Since we have a value for y, let's plug that in:

5x + 6z - 4(-3x - 31) = -48
9x + 2(-3x - 31) - 3z = -68

 

5x + 6z +12x + 124 = -48
9x - 6x - 62 - 3z = -68

 

17x + 6z + 124 = -48

3x - 3z - 62 = -68

 

Look at it now, it looks like solving a system of linear equations. Just need to tidy it up a little first.. We also have a -3z and a +6z, so we can easily use the elimination method when we get there:

17x + 6z = -172

  6x - 6z = -12   <-- 3x - 3z = -6

23x = -184

x = -8

 

Now that we have x, we can start working on the other variables:

y = -3 * -8 - 31

y = 24 - 31 = -7

 

5(-8) + 6z - 4(-7) = -48

-40 + 6z + 28 = -48

6z = -36

z = -6

 

Now we check our answer by putting the values into the other equation:

9(-8) + 2(-7) - 3(-6) = -68

-72 + (-14) - (-18) = -68

-72 + 4 = -68

-68 = -68