if x^2 - y^2 = 77 and x + y=11 what is the value of x?

x-y = (x^2-y^2)/(x+y) = 77/11 = 7

So, now we have

x+y=11
x-y=7

That help?

To find the value of x, we can use the given equations and solve them simultaneously. Let's solve them step-by-step.

Step 1: We have the equations x^2 - y^2 = 77 and x + y = 11.

Step 2: Rearrange the second equation to solve for y by subtracting x from both sides: y = 11 - x.

Step 3: Substitute the value of y from step 2 into the first equation: x^2 - (11 - x)^2 = 77.

Step 4: Expand the equation: x^2 - (121 - 22x + x^2) = 77.

Step 5: Simplify: x^2 - 121 + 22x - x^2 = 77.

Step 6: Combine like terms: 22x - 121 = 77.

Step 7: Add 121 to both sides: 22x = 198.

Step 8: Divide both sides by 22: x = 9.

Therefore, the value of x is 9.

To find the value of x, we can use the given equations to form a system of equations and then solve for the variables. Let's solve it step by step.

First, let's rearrange the equations and eliminate one of the variables using substitution or elimination method.

We have the following equations:

1) x^2 - y^2 = 77

2) x + y = 11

To eliminate one of the variables, we can rewrite equation 2) as x = 11 - y.

Now we can substitute this value of x in equation 1):

(11 - y)^2 - y^2 = 77

Expanding the equation:

121 - 22y + y^2 - y^2 = 77

Simplifying:

121 - 22y = 77

Next, let's isolate the variable y by subtracting 121 from both sides of the equation:

-22y = 77 - 121

Simplifying:

-22y = -44

Now, let's solve for y by dividing both sides by -22:

y = -44 / -22

y = 2

Now that we have the value of y, we can substitute it back into equation 2) to find x:

x + 2 = 11

Subtracting 2 from both sides of the equation:

x = 11 - 2

x = 9

Therefore, the value of x is 9.