Solve the system of equations. y = -27x + 49 y = x^2 - 16x + 7 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. This gives us -27x + 49 = x^2 - 16x + 7.Rearrange and Form Quadratic: Rearrange the equation to set it to zero and form a quadratic equation. This gives us x^2 - 16x + 27x + 7 - 49 = 0, which simplifies to x^2 + 11x - 42 = 0.Factor Quadratic Equation: Factor the quadratic equation. We are looking for two numbers that multiply to -42 and add up to 11. These numbers are 14 and -3. So the factored form is (x + 14)(x - 3) = 0.Solve for x: Solve for x by setting each factor equal to zero. This gives us x + 14 = 0 or x - 3 = 0. Solving these gives us x = -14 and x = 3.Substitute x Values: Substitute x = -14 into one of the original equations to find the corresponding y value. Using y = -27x + 49 gives us y = -27(-14) + 49, which simplifies to y = 378 + 49 and then y = 427.Find Corresponding y Values: Substitute x = 3 into the same original equation to find the corresponding y value. Using y = -27x + 49 gives us y = -27(3) + 49, which simplifies to y = -81 + 49 and then y = -32.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Solve the system of equations. $\newline$ $y = -27x + 49$ $\newline$ $y = x^2 - 16x + 7$ $\newline$ 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 = -27x + 49

\newline

y = x^2 - 16x + 7

\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 $y$ . This gives us $-27x + 49 = x^2 - 16x + 7$ .
Rearrange and Form Quadratic: Rearrange the equation to set it to zero and form a quadratic equation. This gives us $x^2 - 16x + 27x + 7 - 49 = 0$ , which simplifies to $x^2 + 11x - 42 = 0$ .
Factor Quadratic Equation: Factor the quadratic equation. We are looking for two numbers that multiply to $-42$ and add up to $11$ . These numbers are $14$ and $-3$ . So the factored form is $(x + 14)(x - 3) = 0$ .
Solve for x: Solve for x by setting each factor equal to zero. This gives us $x + 14 = 0$ or $x - 3 = 0$ . Solving these gives us $x = -14$ and $x = 3$ .
Substitute $x$ Values: Substitute $x = -14$ into one of the original equations to find the corresponding $y$ value. Using $y = -27x + 49$ gives us $y = -27(-14) + 49$ , which simplifies to $y = 378 + 49$ and then $y = 427$ .
Find Corresponding y Values: Substitute $x = 3$ into the same original equation to find the corresponding y value. Using $y = -27x + 49$ gives us $y = -27(3) + 49$ , which simplifies to $y = -81 + 49$ and then $y = -32$ .