solve the system of equations for x and y
{ x^2 - 11x -y =-24
x^2 - 11x + y = -24
add the two equations and y drops out:
2x^2-22x = -48
x^2-11x+24 = 0
(x-3)(x-8) = 0
Now just find the y for each x.
if you add both the equations you will get an equation 2(x^2-11x=-24)
solving this equation
x=8 or 3
on solving this equation with values of x we get y=0
To solve this system of equations, we will use the method of elimination.
Step 1: Subtract the second equation from the first equation to eliminate the variable y.
(x^2 - 11x - y) - (x^2 - 11x + y) = (-24) - (-24)
Simplifying, we get:
-2y = 0
Step 2: Solve for y by dividing both sides of the equation by -2.
y = 0
Step 3: Substitute the value of y into one of the original equations to find the value of x. Let's substitute it into the first equation.
x^2 - 11x - 0 = -24
Simplifying, we get:
x^2 - 11x = -24
Step 4: Rearrange the equation to make it a quadratic equation equal to zero.
x^2 - 11x + 24 = 0
Step 5: Factor the quadratic equation, or use the quadratic formula to solve for x.
(x - 3)(x - 8) = 0
Which gives two possible solutions:
x - 3 = 0 -> x = 3
x - 8 = 0 -> x = 8
Therefore, the solution to the system of equations is:
x = 3, y = 0
x = 8, y = 0