Question

solve by elimination
is anyone good at explaining this?
2x-y+z=-2
x+3y-z=10
x+2z = -8

Answer 1

first lets number your equations:
2x-y+z=-2 (1)
x+3y-z=10 (2)
x+2z = -8 (3)
we want to get rid of at least one variable. Now notice that (1) has a "+z" and (2) has a "-z", so adding (1) to (2) gives

3x+2y=8 (4)
and multiplying (2) by 2, then adding it to (3) gives

3x+6y=12 (5)

subtracting (5)-(4) will get rid of the x's:

4y=4
y=1

lets plug that value into (1) and (2). Our modified equations are now
2x-1+z=-2 ->2x+z=-1 (6)
x+3-z=10 -> x-z=7 (7)

get rid of the z again by adding (6) to (7):
3x=6
x=2
now we can solve any equation for z and plug in the values for x=2 and y=1 to find the value of z. Solving (2) for z gives

z=x+3y-10=2+3-10=-5
so
x=2
y=1
z=-5

I know that was long and tedious, but try to follow my explanation closely.
PS: If (hopefully "when") you take Linear Algebra you will learn far easier and more efficient methods for solving these systems, so hold out!