solving the system by addition

Question

{x+y=8

{x-y+2

Answer 1

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

Answer 2

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?