Solve the system of equations. y = x^2 + 40x - 50 y = 40x + 50 Write the coordinates in exact form. Simplify all fractions and radicals. (______,______) (______,______)

Set Equations Equal: Set the two equations equal to each other since they both equal y. y = x^2 + 40x - 50 y = 40x + 50 So, x^2 + 40x - 50 = 40x + 50.Subtract to Zero: Subtract 40x + 50 from both sides to set the equation to zero. x^2 + 40x - 50 - 40x - 50 = 0 This simplifies to x^2 - 100 = 0.Factor Quadratic Equation: Factor the quadratic equation. x^2 - 100 = (x + 10)(x - 10) = 0Solve for x: Solve for x by setting each factor equal to zero. x + 10 = 0 or x - 10 = 0 This gives us x = -10 or x = 10.Substitute x Values: Substitute x = -10 into one of the original equations to find the corresponding y value. Using y = 40x + 50, we get y = 40(-10) + 50 = -400 + 50 = -350.Find Corresponding y: Substitute x = 10 into one of the original equations to find the corresponding y value. Using y = 40x + 50, we get y = 40(10) + 50 = 400 + 50 = 450.Write Coordinate Points: Write the solution as coordinate points. The coordinate points are (-10, -350) and (10, 450).

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Solve the system of equations. $\newline$ $y = x^2 + 40x - 50$ $\newline$ $y = 40x + 50$ $\newline$ Write the coordinates in exact form. Simplify all fractions and radicals. $\newline$ (,) $\newline$ (,)

View step-by-step help

Home

Math Problems

Algebra 2

Solve a nonlinear system of equations

Full solution

Q. Solve the system of equations.

\newline

y = x^2 + 40x - 50

\newline

y = 40x + 50

\newline

Write the coordinates in exact form. Simplify all fractions and radicals.

\newline

(______,______)

\newline

(______,______)

Set Equations Equal: Set the two equations equal to each other since they both equal $y$ . $y = x^2 + 40x - 50$ $y = 40x + 50$ So, $x^2 + 40x - 50 = 40x + 50$ .
Subtract to Zero: Subtract $40x + 50$ from both sides to set the equation to zero. $\newline$ $x^2 + 40x - 50 - 40x - 50 = 0$ $\newline$ This simplifies to $x^2 - 100 = 0$ .
Factor Quadratic Equation: Factor the quadratic equation. $x^2 - 100 = (x + 10)(x - 10) = 0$
Solve for x: Solve for x by setting each factor equal to zero. $\newline$ $x + 10 = 0$ or $x - 10 = 0$ $\newline$ This gives us $x = -10$ or $x = 10$ .
Substitute $x$ Values: Substitute $x = -10$ into one of the original equations to find the corresponding $y$ value. $\newline$ Using $y = 40x + 50$ , we get $y = 40(-10) + 50 = -400 + 50 = -350$ .
Find Corresponding y: Substitute $x = 10$ into one of the original equations to find the corresponding y value. $\newline$ Using $y = 40x + 50$ , we get $y = 40(10) + 50 = 400 + 50 = 450$ .
Write Coordinate Points: Write the solution as coordinate points. $\newline$ The coordinate points are $(-10, -350)$ and $(10, 450)$ .