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solving the system by addition

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2 Answers

The whole trick with this system is add the equations to get x, subtract the equations to get y
x+y=8
x-y=2
add and get
2x=10, x=5
subtract and get
2y=6, y=3
Hi Danielle;
I think that the { is incorrectly placed.  I will proceed anyway.  If I am mistaken, please let me know.
{x+y=8
x+y=8
{x-y+2
I am also assuming this is x-y=2
x-y=2
 
The addition method requires only one variable.  So let's isolate one variable in each equation.  I randomly choose the y.
x+y=8
y=8-x
 
x-y=2
-y=2-x
y=x-2
Do you understand the last revision?  I multiplied both sides by -1 to eliminate the negative sign and completely isolate y.
 
8-x=x-2
Let's add 2 to both sides...
2+8-x=x-2+2
10-x=x
Let's add x to both sides...
x+10-x=x+x
10=2x
Let's divide both sides by 2...
10/2=2x/2
5=x
 
Let's solve for y...
x+y=8
5+y=8
y=3
 
x-y=2
5-y=2
y=3
 
I hope this helps.  Please let me know either way.  Did I make correct assumptions?