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.

Question

y=x^2+2x
y=3x+20

Answer 1

To solve this system of equations, we will set the two equations equal to each other:

x^2 + 2x = 3x + 20

Next, we will rearrange the equation to set it equal to zero:

x^2 + 2x - 3x - 20 = 0
x^2 - x - 20 = 0

Now, we will factor the quadratic equation:

(x - 5)(x + 4) = 0

Setting each factor to zero and solving for x, we get:

x - 5 = 0 or x + 4 = 0
x = 5 x = -4

Now that we have the x-values, we can plug them back into one of the original equations to find the corresponding y-values. Let's use y = x^2 + 2x:

If x = 5:
y = 5^2 + 2(5) = 25 + 10 = 35
So, one solution is (5, 35).

If x = -4:
y = (-4)^2 + 2(-4) = 16 - 8 = 8
So, the other solution is (-4, 8).

Therefore, the solutions to the system of equations are (5, 35) and (-4, 8).