xy = 8
y = x + 2
Brian,
Stop switching names. All you have to do is substitute.
x(x+2)=8
x^2+2x=8
x^2+2x-8=0
Use the quadratic formula and double check my work.
O.K. It's time for you to learn from the many answers you've received under your many aliases today.
Solve this problem yourself and someone may check it for you.
Please do not post any more similar questions -- under any name -- unless you show us your work.
To solve the equations xy = 8 and y = x + 2, we can substitute the value of x from the second equation into the first equation.
Given that y = x + 2, we can replace x with (y - 2) in the equation xy = 8.
Substituting, we get (y - 2)y = 8.
Expanding, we have y^2 - 2y = 8.
Rearranging the equation, we have y^2 - 2y - 8 = 0.
This is a quadratic equation, which can be factored or solved using the quadratic formula:
y^2 - 2y - 8 = 0
Factoring, we find: (y - 4)(y + 2) = 0.
Setting each factor equal to zero, we have two possible solutions:
1) y - 4 = 0, which gives y = 4.
2) y + 2 = 0, which gives y = -2.
Now that we have the values of y, we can substitute them back into the equation y = x + 2 to find the corresponding values of x.
For y = 4, substituting into y = x + 2, we get 4 = x + 2. Solving for x, we find x = 2.
For y = -2, substituting into y = x + 2, we get -2 = x + 2. Solving for x, we find x = -4.
Therefore, the solutions to the equations xy = 8 and y = x + 2 are:
(x, y) = (2, 4) and (-4, -2).