| I'll show you how to do it for the first equation, then you should be able to do the others yourself:
3x-y=7
5x+2y=8
From the first line:
3x-y=7
we can calculate the value of y in function of x:
3x=7+y
or y+7=3x
or y=3x-7
We fill in this value in the second line which means that we replace y by (3x-7):
5x+2(3x-7)=8
or 5x+6x-14=8
or 11x-14=8
or 11x=14+8
or 11x=22
or x=2
This exact value of x can now be reintroduced in one of the equations to calculate y. It doesn't matter which one, so we take the first one:
3x-y=7
or 3*2-y=7
or 6-y=7
or 6=7+y
or y=6-7
or y=(-1)
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If you have 3 variables, you first take one equation to express the value of one variable in function of the two other variables, and introduce that value in a second equation to eliminate the next variable.
x+y+z=6
x+2y+3z=14
x+3y+7z=28
from the first:
x=6-y-z remember this one for later, call it (1)
fill this in in the second equation:
6-y-z+2y+3z=14
or: 6+y+2z=14
or y+2z=8
or y=(8-2z) remember this one for later, call it (2)
Remembering (1), we replace y in there by (8-2z):
x=6-(8-2z)-z
or x=6-8+2z-z
or x=z-2 remember this one, call it (3).
(2) and (3) both show the values for x and y expressed in function of z.
We fill them in in the third equation:
x+3y+7z=28
(z-2)+3(8-2z)+7z=28
or z-2+24-6z+7z=28
2z+22=28
z=3
Filling in this value of z in (2) and (3) will give you the values of x and y:
x=3-2
or x=1
y=(8-6)
or y=2
Result: x=1 y=2 z=3 | 
Linear Mode
