Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. Solve the system of equations algebraically. Show all of your steps. y=x2+2x y=3x+20
To solve this system of equations algebraically, we will set the two equations equal to each other and solve for the value of x.
x^2 + 2x = 3x + 20
x^2 + 2x - 3x - 20 = 0
x^2 - x - 20 = 0
Now, we need to factor the quadratic equation:
(x - 5)(x + 4) = 0
Setting each factor to zero:
x - 5 = 0 or x + 4 = 0
x = 5 or x = -4
Now that we have the values of x, we can substitute them back into one of the original equations to find the corresponding y-values.
For x = 5:
y = (5)^2 + 2(5) = 25 + 10 = 35
For x = -4:
y = (-4)^2 + 2(-4) = 16 - 8 = 8
Therefore, the solution to the system of equations is (5, 35) and (-4, 8).