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Question

Solve the system of equations algebraically. Show all of your steps.
y = x²+2x
y = 3x + 20

Answer 1

To solve this system of equations algebraically, we will set the two equations equal to each other since they both equal y:

x² + 2x = 3x + 20

Next, we will move all terms to one side to set the equation equal to zero:

x² + 2x - 3x - 20 = 0

Simplify the equation:

x² - x - 20 = 0

Now, we will 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, plug these x-values back into either of the original equations to solve for y:

For x = 5:

y = (5)² + 2(5)
y = 25 + 10
y = 35

For x = -4:

y = (-4)² + 2(-4)
y = 16 - 8
y = 8

Therefore, the solutions to the system of equations are:
x = 5, y = 35
x = -4, y = 8