Question

Solve the system by elimination.
x + 5y - 4z = -10
2x - y + 5z = -9
2x - 10y - 5z = 0

I've been having trouble with these problems, can someone help me with this practice problem?

Answer 1

x + 5y - 4z = -10
2x - y + 5z = -9
2x - 10y - 5z = 0

-1(x + 5y - 4z = -10)
5(2x - y + 5z = -9)
-1(2x - 10y - 5z = 0)

-x - 5y + 4z = 10
10x - 5y + 25z = -45
-2x + 10y + 5z = 0
Add the equations

7x + 0y + 34z = -35

7x + 34z = -35

Do this until you can solve for x, y, or z. Then use your x, y, or z value to find the other two.

It is tedious.

Answer 2

Wait what did you do after the original equations?

Answer 3

I scaled them to obtain values that were suitable for eliminating a variable. I multiplied each part of the equation to get to the point where when I added them, the y would be eliminated and I would be left with x and z. This gets me closer to solving for a single variable than having x, y, and z.