Question

Solve for x and y:

2x + y = 1
x - y = 8

PLEASE HELP. and show work.(:

Answer 1

In a set of simultaneous equations, just add these two equations so as to cancel one of the terms. In this case that is easy to do; if they don't automatically add to cancel one of the variables, then multiply one or both of the equations to make them cancel.
2x+y=1
x-y=8
=============
adding we obtain
3x=9
x = 3
Now substitute the 3 for x into either of the equations; e.g.
x-y=8
3-y=8
-y=8-3=5
y=-5
Now check your solution to see that x = 3 and y=-5 will satisfy BOTH equations.
x-y=8
3-(-5)=8
3+5=8
8=8
======
Now the other equation.
2x+y=1
2(3)+(-5)=1
6-5=1
1=1
both check
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But what if one of the variables won't cancel. Here is what you can do.
2x+y=1
x-y=8
=========
Now multiply equation 1 by -1; follow that by multiplying equation 2 by 2.
-x+y=-8 and
-2x+2y=-16
Now add in equation 1 like so
-2x+2y=-16
2x+y=1
=============
3y=-15
y=-5 which is the answer we obtained above. Now substitute -5 into either equation and solve for x.
I hope this helps.