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6x+4y= 10
x-y= 5

Solve equation for x
x = y+5

Then SUBSTITUTE the expression in the other equation

6x+4y=10
6(y+5)+4y= 10
y=-2

After you solve for y, insert y into the first equation and solve for x

x-y=5
x-(-2)=5
x+2=5
x= 3

Your final answer is
(3,-2)

  5x-4y=20
-10x+16y= 8

Multiply the first equation by 2 so that the X variables  cancel out

10x-8y = 40
-10x+16y = 8
8y = 48
y = 6

y-x=6
2x+y=-3

First you have to but the equations into the y=mx+b form

y=x+6
y=-2x-3

Now GRAPH the equations

After you graph the equations find the point of intersection and that will be your answer

Your final answer is
(-3,3)

Time to try out what you have learned in a word problem:

The pricing structures for two competing cellular phone companies are:
     Company A charges $10/mo base fee plus $.10/minute   usage charge    

     Company B charges $.35/minute usage charge and NO base fee

    How many minutes would you have to use each month for the payments to be the same?

First you would put the charges into y=mx+b form:
          Company A-y=.10x+10 
     Company B-y=.35x

Now graph the two equations

The two lines intersect at point (40,14)

You final answer is

You would have to use 40 minutes each month for the two payments to be equal.