note: evter your answer and show all the steps that you use to solve this problem in the space provided.

Question

solve the system of equations algebraically. show all of your steps.

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

Answer 1

To solve the system of equations algebraically, we can set both equations equal to each other:

x^2 + 2x = 3x + 20

Now, let's rearrange the equation to put it in standard quadratic form:

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

Combining like terms:

x^2 - x - 20 = 0

Now, we can factor the equation:

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

Setting each factor equal to zero:

x - 5 = 0 or x + 4 = 0

Solving for x:

x = 5 or x = -4

Now, we substitute these values of x back into either equation to find the corresponding values of y.

For x = 5:
y = (5)^2 + 2(5)
y = 25 + 10
y = 35

So, one solution is (x, y) = (5, 35).

For x = -4:
y = (-4)^2 + 2(-4)
y = 16 - 8
y = 8

So, the other solution is (x, y) = (-4, 8).

Therefore, the system of equations has two solutions: (5, 35) and (-4, 8).