459,453 views
16 votes
16 votes
Y equals X square + 2x y equals 3x + 20 how do I solve this

User Fred Johnson
by
2.2k points

1 Answer

19 votes
19 votes

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)

User Paluh
by
2.4k points