Solve these simultaneous equations. x^2 - xy=35 and x-y=5 ?

To solve these simultaneous equations, we can use substitution or elimination method.

Given equations:
1) x^2 - xy = 35
2) x - y = 5

From equation 2, we can express y in terms of x:
y = x - 5

Substitute y = x - 5 into equation 1:
x^2 - x(x-5) = 35
x^2 - x^2 + 5x = 35
5x = 35
x = 7

Now substitute x = 7 into equation 2 to find y:
7 - y = 5
y = 2

Therefore, the solution to the simultaneous equations is x = 7 and y = 2.

Step 1: Solve for y in the second equation.

x - y = 5
-y = 5 - x
y = x - 5

Step 2: Substitute the expression for y into the first equation.

x^2 - x(x - 5) = 35
x^2 - x^2 + 5x = 35
5x = 35
x = 7

Step 3: Substitute the value of x back into the expression for y.

y = x - 5
y = 7 - 5
y = 2

Therefore, the solution to the simultaneous equations is x = 7 and y = 2.