Solve using elimination. x + 6y = –15 9x + 6y = 9 (_____, _____)

Write Equations: Write down the system of equations to identify the method to use for solving. x + 6y = –15 9x + 6y = 9 We will use the elimination method to solve this system of equations.Subtract Equations: Subtract the first equation from the second equation to eliminate the variable y. (9x + 6y) - (x + 6y) = 9 - (–15) This simplifies to: 9x + 6y - x - 6y = 9 + 15Combine Terms: Combine like terms to find the value of x. 9x - x + 6y - 6y = 24 8x = 24Divide by 8: Divide both sides of the equation by 8 to solve for x. 8x / 8 = 24 / 8 x = 3Substitute x: Substitute the value of x into one of the original equations to solve for y. Using the first equation: x + 6y = –15 3 + 6y = –15Isolate y: Subtract 3 from both sides of the equation to isolate the term with y. 3 + 6y - 3 = –15 - 3 6y = –18Divide by 6: Divide both sides of the equation by 6 to solve for y. 6y / 6 = –18 / 6 y = –3

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Solve using elimination. $\newline$ $x + 6y = -15$ $\newline$ $9x + 6y = 9$ $\newline$ (_, _)

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Grade 8

Solve a system of equations using elimination

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Q. Solve using elimination.

\newline

x + 6y = -15

\newline

9x + 6y = 9

\newline

(_____, _____)

Write Equations: Write down the system of equations to identify the method to use for solving. $\newline$ $x + 6y = -15$ $\newline$ $9x + 6y = 9$ $\newline$ We will use the elimination method to solve this system of equations.
Subtract Equations: Subtract the first equation from the second equation to eliminate the variable $y$ . $(9x + 6y) - (x + 6y) = 9 - (–15)$ This simplifies to: $9x + 6y - x - 6y = 9 + 15$
Combine Terms: Combine like terms to find the value of $x$ . $9x - x + 6y - 6y = 24$ $8x = 24$
Divide by $8$ : Divide both sides of the equation by $8$ to solve for x. $\newline$ $\frac{8x}{8} = \frac{24}{8}$ $\newline$ $x = 3$
Substitute $x$ : Substitute the value of $x$ into one of the original equations to solve for $y$ . Using the first equation: $x + 6y = -15$ $3 + 6y = -15$
Isolate y: Subtract $3$ from both sides of the equation to isolate the term with $y$ . $\newline$ $3 + 6y - 3 = -15 - 3$ $\newline$ $6y = -18$
Divide by $6$ : Divide both sides of the equation by $6$ to solve for $y$ . $\frac{6y}{6} = \frac{-18}{6}$ $y = -3$