Question

Solve each system by substitution

{3x+y-2z=22
{x+5y+z=4
{x=-3z

Answer 1

The assumption here is that x y and z have the same values in all three equations. You want to find three numbers, that every occurrence of x is replaced by the first, y by the second, and z by the third, in each of the three equations, the three equalities will still hold.

The idea of solving by substitution is that, through algebraic manipulation, you find the value of (for example), x in terms of y and z in one equation (or the value of y in terms of x and z, or z in terms of x and y). You then replace x with this value in one of the other equations. Then, you manipulate that equation to get the value of y in terms of z, or z in terms of y. Then, in the third equation, you rewrite x in terms of y and z, and then rewrite the y's, even the new ones you create with replacing x, in terms of z. Then, you can shuffle stuff around to find the value of z.

This value will be the same in all three equations. It's kind of tricky to explain why, but it involves the fact that you used all three equations to come up with the value.

You can write this value to the side, and replace the z's with that value in all three equations. Then you can do the same thing to figure out y, and then finally for x.

Answer 2

I need someone to walk me through the process