Solve the system of equations. y = 21x - 10 y = x^2 + 35x - 25 Write the coordinates in exact form. Simplify all fractions and radicals. (______,______) (______,______)

Substitute y into second equation: Substitute y from the first equation into the second equation. Since y = 21x - 10 and y = x^2 + 35x - 25, we can set them equal to each other: 21x - 10 = x^2 + 35x - 25.Rearrange and solve for x: Rearrange the equation to set it to zero and solve for x: x^2 + 35x - 25 - (21x - 10) = 0. This simplifies to x^2 + 14x - 15 = 0.Factor the quadratic equation: Factor the quadratic equation: (x + 15)(x - 1) = 0. This gives us two possible solutions for x: x = -15 or x = 1.Solve for y with x = -15: Solve for y using the first equation y = 21x - 10 with x = -15: y = 21(-15) - 10 = -315 - 10 = -325.Solve for y with x = 1: Solve for y using the first equation y = 21x - 10 with x = 1: y = 21(1) - 10 = 21 - 10 = 11.Write solution as coordinate points: Write the solution as coordinate points. The coordinate points are (-15, -325) and (1, 11).

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Solve the system of equations. $\newline$ $y = 21x - 10$ $\newline$ $y = x^2 + 35x - 25$ $\newline$ Write the coordinates in exact form. Simplify all fractions and radicals. $\newline$ (,) $\newline$ (,)

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Algebra 2

Solve a nonlinear system of equations

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Q. Solve the system of equations.

\newline

y = 21x - 10

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y = x^2 + 35x - 25

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

\newline

(______,______)

\newline

(______,______)

Substitute $y$ into second equation: Substitute $y$ from the first equation into the second equation. Since $y = 21x - 10$ and $y = x^2 + 35x - 25$ , we can set them equal to each other: $21x - 10 = x^2 + 35x - 25$ .
Rearrange and solve for x: Rearrange the equation to set it to zero and solve for $x$ : $x^2 + 35x - 25 - (21x - 10) = 0$ . This simplifies to $x^2 + 14x - 15 = 0$ .
Factor the quadratic equation: Factor the quadratic equation: $(x + 15)(x - 1) = 0$ . This gives us two possible solutions for $x$ : $x = -15$ or $x = 1$ .
Solve for $y$ with $x = -15$ : Solve for $y$ using the first equation $y = 21x - 10$ with $x = -15$ : $y = 21(-15) - 10 = -315 - 10 = -325$ .
Solve for $y$ with $x = 1$ : Solve for $y$ using the first equation $y = 21x - 10$ with $x = 1$ : $y = 21(1) - 10 = 21 - 10 = 11$ .
Write solution as coordinate points: Write the solution as coordinate points. The coordinate points are $(-15, -325)$ and $(1, 11)$ .