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#7-8, use eliminati

{:[2x+6y=12],[-5x-6y=-3]:}

\# $7$ $-8$ , use eliminati $\newline$ $\begin{array}{r} 2 x+6 y=12 \\ -5 x-6 y=-3 \end{array}$

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Write a quadratic function from its x-intercepts and another point

Full solution

Q. \#

7

-8

, use eliminati

\newline

\begin{array}{r} 2 x+6 y=12 \\ -5 x-6 y=-3 \end{array}

Add Equations: Add the two equations to eliminate $y$ . $(2x + 6y) + (-5x - 6y) = 12 + (-3)$
Simplify Equation: Simplify the equation. $2x - 5x = 12 - 3$
Combine Terms: Combine like terms. $\newline$ $-3x = 9$
Divide to Solve $x$ : Divide both sides by $-3$ to solve for $x$ . $x = \frac{9}{-3}$
Calculate $x$ : Calculate the value of $x$ . $x = -3$
Substitute $x$ for $y$ : Substitute $x = -3$ into one of the original equations to solve for $y$ . Let's use the first equation: $2x + 6y = 12$ $2(-3) + 6y = 12$
Simplify Equation: Simplify the equation. $-6 + 6y = 12$
Add to Both Sides: Add $6$ to both sides. $\newline$ $6y = 12 + 6$
Combine Terms: Combine like terms. $\newline$ $6y = 18$
Divide to Solve $y$ : Divide both sides by $6$ to solve for $y$ . $\newline$ $y = \frac{18}{6}$
Calculate $y$ : Calculate the value of $y$ . $y = 3$

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