SOLUTION: Solve the system of 3 linear equations containing 3 unknowns. I can't bring myself to understand how to do these. Please provide steps; it would be greatly appreciated! x-y=5

Question 741556: Solve the system of 3 linear equations containing 3 unknowns. I can't bring myself to understand how to do these. Please provide steps; it would be greatly appreciated!
x-y=5
5x-8z=35
5y+z=10
Answer by josgarithmetic(39618) (Show Source): You can put this solution on YOUR website!
Do you want to use matrix or use substitution?

Try substitution. Solve the first equation for x:
x=5+y.

Substitute this expression for x into the second equation:
5x-8z=35
5(5+y)-8z=35
25+5y-8z=35
5y-8z=10

You still have the last equation which is in variables y and z, so you have your choice of either taking the one you just found or the last equation and solve for and substitute for y or for z.
I'll try taking these two:
5y-8z=10 AND 5y+z=10
and solve the first one for y and substitute this into the next one:
5y=10+8z
y=2+8z/5
Do the substitution into the other equation:
5y+z=10
5(2+8z/5)+z=10
10+8z+z=10
9z=0
z=0.

Backsubstutite in any equation to find another variable.
5y+0=10, the last of the given equations
5y=10
y=2.

Backsubstitute into any equation which has y; only one good one to choose; the first given equation.
x-y=5
x-2=5
x=5+2
x=7

SOLUTION:
x=7, y=2, z=0.

After looking at the given system again, it seems like elimination might be easier for the system.
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