Solve the system of equations. y = 3x^2 + 14x - 21 y = 14x + 27 Write the coordinates in exact form. Simplify all fractions and radicals. (______,______) (______,______)

Set Equations Equal: We have the following system of equations: y = 3x^2 + 14x - 21 y = 14x + 27 To find the solution, we need to set the two equations equal to each other because they both equal y. 3x^2 + 14x - 21 = 14x + 27Simplify by Subtracting: Subtract 14x from both sides to start simplifying the equation. 3x^2 + 14x - 21 - 14x = 14x + 27 - 14x 3x^2 - 21 = 27Isolate Quadratic Term: Add 21 to both sides to isolate the quadratic term. 3x^2 - 21 + 21 = 27 + 21 3x^2 = 48Solve for x^2: Divide both sides by 3 to solve for x^2. 3x^2 / 3 = 48 / 3 x^2 = 16Find x: Take the square root of both sides to solve for x. sqrt(x^2) = sqrt(16) x = 4 or x = -4Substitute x=4: Substitute x = 4 into the second equation y = 14x + 27 to find the corresponding y-value. y = 14(4) + 27 y = 56 + 27 y = 83Substitute x=-4: Substitute x = -4 into the second equation y = 14x + 27 to find the corresponding y-value. y = 14(-4) + 27 y = -56 + 27 y = -29Write Coordinates: Write the coordinates in exact form. For x = 4, y = 83, so the first coordinate is (4, 83). For x = -4, y = -29, so the second coordinate is (-4, -29).

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Solve the system of equations. $\newline$ $y = 3x^2 + 14x - 21$ $\newline$ $y = 14x + 27$ $\newline$ Write the coordinates in exact form. Simplify all fractions and radicals. $\newline$ (,) $\newline$ (,)

View step-by-step help

Home

Math Problems

Algebra 1

Solve a system of linear and quadratic equations

Full solution

Q. Solve the system of equations.

\newline

y = 3x^2 + 14x - 21

\newline

y = 14x + 27

\newline

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

\newline

(______,______)

\newline

(______,______)

Set Equations Equal: We have the following system of equations: $\newline$ $y = 3x^2 + 14x - 21$ $\newline$ $y = 14x + 27$ $\newline$ To find the solution, we need to set the two equations equal to each other because they both equal $y$ . $\newline$ $3x^2 + 14x - 21 = 14x + 27$
Simplify by Subtracting: Subtract $14x$ from both sides to start simplifying the equation. $\newline$ $3x^2 + 14x - 21 - 14x = 14x + 27 - 14x$ $\newline$ $3x^2 - 21 = 27$
Isolate Quadratic Term: Add $21$ to both sides to isolate the quadratic term. $\newline$ $3x^2 - 21 + 21 = 27 + 21$ $\newline$ $3x^2 = 48$
Solve for $x^2$ : Divide both sides by $3$ to solve for $x^2$ . $\newline$ $\frac{3x^2}{3} = \frac{48}{3}$ $\newline$ $x^2 = 16$
Find $x$ : Take the square root of both sides to solve for $x$ . $\sqrt{x^2} = \sqrt{16}$ $x = 4 \text{ or } x = -4$
Substitute $x=4$ : Substitute $x = 4$ into the second equation $y = 14x + 27$ to find the corresponding y-value. $\newline$ $y = 14(4) + 27$ $\newline$ $y = 56 + 27$ $\newline$ $y = 83$
Substitute $x=-4$ : Substitute $x = -4$ into the second equation $y = 14x + 27$ to find the corresponding y-value. $\newline$ $y = 14(-4) + 27$ $\newline$ $y = -56 + 27$ $\newline$ $y = -29$
Write Coordinates: Write the coordinates in exact form. $\newline$ For $x = 4$ , $y = 83$ , so the first coordinate is $(4, 83)$ . $\newline$ For $x = -4$ , $y = -29$ , so the second coordinate is $(-4, -29)$ .