Thread: Solving systems of equations

Hi,

I'm looking for help with solving these two systems of equations (any method can be used):

1.

-4x - 5y - 8z = 268
-10x + 7y + 6z = -786
-12x + 9y - 2z = -548

2.

-5x - 4y + 12z = -140
9x - 8y + z = -649
3x - 2y + 6z = -290

Thanks for your help.

What method have you chosen? Where are you stuck?

Please be complete. Thank you!

Originally Posted by stapel

What method have you chosen? Where are you stuck?

Please be complete. Thank you!

I'm pretty sure what I used was substitution when trying to solve them. Here's my work so far for number 2:

-5x - 4y + 12z = -140
9x - 8y + z = -649
3x - 2y + 6z = -290

I multiplied row 1 by -1

5x + 4y - 12z = 140

Then I multiplied row 3 by 2

6x - 4y + 12z = -580

Added them together to get:

11x = -440, which means x = -40

What I did next was substitute -40 in for x in one of the equations,

9(-40) – 8y + z = -649
-360 – 8y + z = -649
-8y + z = - 289
z = 8y – 289

is what I got. From there I'm a little unsure as to how I should continue.

Once you get past two equations in two variables, it's often better to add equations together. For instance, you have:







I see right away that I can multiply by and add this to to get:







Because I really would rather leave fractions until the end, and since twice three is close to five, I'll multiply by and add the result to . This gives me:







Now I'll multiply by and add the result to . This gives me:







For simplicity's sake, I'll divide by to get:








The last two rows are now a system of two equations in two unknowns. Solve that, plug the values for and into the first equation, and simplify to find the value of .