What is the solution to the following system of equations?

Question

x-4y+z = -24

3x+2y-3z = 10

2x-5y+8z = 3

x+z = 6

Answer 1

Start with the simplest...

x+z=6.

Solve for z, let's say. z=6-x

Plug that into x-4y+z=-24. So that x-4y+(6-x)=-24.

This is convenient because the x's cancel and we can solve directly for y. y=7.5

Now, substitute both the value for y and the expression for z, 6-x, into 2x-5y+48-8z=3 and solve for x.

2x-5(7.5)+48-8(6-x)=3.

You now have values for x, y, and z. Try plugging them into the fourth equation 3x+2y-3z=10 and see if it works. If it doesn't, there is no solution. (Spoiler alert.)