What are the solutions to the following system of equations? Select the correct answer below. y = x2 − 2x + 4 8x + y = 20

Given the systems of equation:

y =x^2 + 2x + 8x

8x + y = 20 or y = 20 -8x

Solve for the solutions of the system.

Solution:

In order to solve for the solutions of the system, we equate the given into one single solution.

x^2 + 2x + 8x = 20 - 8x

Transpose 20 - 8x on the other side of the equation, note that when transposing a number, the sign changes.

x^2 + 2x + 8x - 20 + 8x = 0

x^2 + 18x - 20 = 0

a = 1

b= 18

c = -20

In order to solve for the roots of an equation, we simply must look at the 2nd and 3rd values. First, we must think of two numbers that when added, the answer is 18, and when multiplied, the answer is -20 Hence, if we are unable to find the number, we will use the quadratic formula. 

The Quadratic formula:

x = −b ± √(b^2 − 4ac)/2a

is used to solve quadratic equations where a ≠ 0, in the form
ax^2+bx+c=0

When b^2−4ac=0 there is one real root.

When b^2−4ac>0 there are two real roots.

When b^2−4ac<0 there are no real roots, only a complex number.

Substitute the given values to the quadratic formula.
x = −b ± √(b^2 − 4ac)/2a
x = −18 ± √((18)^2 − 4(1)(-20))/2(1)
x = −18 ± √((324 +80))/2
x = −18 ± √(404)/2
x = −18 ± 20.1 / 2

Solve for + - individually.

x = −18 + 20.1 / 2

x = 2.1 / 2

x = 1.05

x = −18 - 20.1 / 2

x = -38.1 / 2

x = -19.05

Final answer:

x = 1.05

x = -19.05