Solve the system of equations algebraically show all of your steps

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

1 answer

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

x^2 + 2x = 3x + 20

Next, we want to isolate the variable x, so we should subtract 3x from both sides:

x^2 - x = 20

Now, we can rewrite the equation as a quadratic equation:

x^2 - x - 20 = 0

Now, we need to factor the quadratic equation:

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

Setting each factor equal to zero:

x - 5 = 0
x = 5

x + 4 = 0
x = -4

Now that we have found the values for x, we can substitute them back into one of the original equations to find the corresponding values for y.

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 x = 5, y = 35 and x = -4, y = 8.