# Math Help - solve equation

1. ## solve equation

If x^2-y^2=77 and x+y=11, what is the value of x?
I don't get why the correct answer is 9. Thanks in advance

2. Hello,
Originally Posted by fabxx
If x^2-y^2=77 and x+y=11, what is the value of x?
I don't get why the correct answer is 9. Thanks in advance
Note that $77=x^2-y^2=({\color{red}x+y})(x-y)$
You'll get an equation : (x-y)=... and associated to the x+y=11 one, you'll have a linear system of two equations.

3. But if you do like that, won't you have x in terms of y? I need a value of x with a number. (

4. Originally Posted by fabxx
But if you do like that, won't you have x in terms of y? I need a value of x with a number. (
Get the equations first.

1/ Simplify (x+y)(x-y)=77 thanks to the equation x+y=11. This gives a second equation.
2/ Write the system x+y=11 and x-y=... and simplify the y's.

5. Ok, i'll give it a try.
(x+y)(x-y)=77 and because (x+y)=11 so 11(x-y)=77
Therefore, 11x-11y=77
so, x-y=7
also, from before, x+y=11
so, I try to get rid of the y
-2y=-4
y=2
sub y=2 into equation
x+2=11
so x=9!!

Thank you so much !! You helped a lot

6. Originally Posted by fabxx
Ok, i'll give it a try.
(x+y)(x-y)=77 and because (x+y)=11 so 11(x-y)=77
Therefore, 11x-11y=77
so, x-y=7
also, from before, x+y=11
so, I try to get rid of the y
-2y=-4
y=2
sub y=2 into equation
x+2=11
so x=9!!

Thank you so much !! You helped a lot
It is correct ! though long !

I'll show you how I would do (and I guess it's faster...)

(x+y)(x-y)=77
11(x-y)=77
Divide by 11 :
x-y=7