Answer:
(5, 35) and (-4, 8)
Step-by-step explanation:
The initial system of equations is:
y = x² + 2x
y = 3x + 20
So, we will substitute y = x² + 2x on the second equation to get:
y = 3x + 20
x² + 2x = 3x + 20
Now, let's rewrite the equation as:
x² + 2x - 3x = 3x + 20 - 3x
x² - x = 20
x² - x - 20 = 20 - 20
x² - x - 20 = 0
Then, to factorize the expression, we need to find two numbers that multiply to -20 and sum to -1. These numbers are -5 and 4, so the equation is equivalent to:
x² - x - 20 = 0
(x - 5)(x + 4) = 0
So, the solutions of the equation are:
x - 5 = 0
x - 5 + 5 = 0 + 5
x = 5
or
x + 4 = 0
x + 4 - 4 = 0 - 4
x = -4
Finally, replace x by 5 and x by 4, to get the coordinates of y, so:
If x = 5, then:
y = 3x + 20 = 3(5) + 20 = 35
If x = -4, then:
y = 3x + 20 = 3(-4) + 20 = 8
Therefore, the solutions of the equations are the points (5, 35) and (-4, 8)