Solve using elimination. 9x − 6y = –18 9x − 7y = –15 (_____, _____)

Set Up Equations: First, we need to set up the equations in a way that allows us to eliminate one of the variables by subtracting one equation from the other. The given equations are: 9x − 6y = –18 9x − 7y = –15Eliminate Variable x: To eliminate the variable x, we can subtract the second equation from the first equation. (9x − 6y) − (9x − 7y) = (–18) − (–15)Perform Subtraction: Perform the subtraction: 9x − 9x − 6y + 7y = –18 + 15 This simplifies to: 0x + y = –3 So, y = –3Substitute y into Equation: Now that we have the value of y, we can substitute it into one of the original equations to find the value of x. Let's use the first equation: 9x − 6y = –18 Substitute y = –3 into the equation: 9x − 6(–3) = –18Solve for x: Solve for x: 9x + 18 = –18 9x = –18 − 18 9x = –36 x = –36 / 9 x = –4Final Values: We have found the values of x and y that solve the system of equations: x = –4, y = –3

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Solve using elimination. $\newline$ $9x - 6y = -18$ $\newline$ $9x - 7y = -15$ $\newline$ (_, _)

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Grade 8

Solve a system of equations using elimination

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Q. Solve using elimination.

\newline

9x - 6y = -18

\newline

9x - 7y = -15

\newline

(_____, _____)

Set Up Equations: First, we need to set up the equations in a way that allows us to eliminate one of the variables by subtracting one equation from the other. $\newline$ The given equations are: $\newline$ $9x − 6y = −18$ $\newline$ $9x − 7y = −15$
Eliminate Variable $x$ : To eliminate the variable $x$ , we can subtract the second equation from the first equation. $(9x − 6y) − (9x − 7y) = (−18) − (−15)$
Perform Subtraction: Perform the subtraction: $\newline$ $9x - 9x - 6y + 7y = -18 + 15$ $\newline$ This simplifies to: $\newline$ $0x + y = -3$ $\newline$ So, $y = -3$
Substitute $y$ into Equation: Now that we have the value of $y$ , we can substitute it into one of the original equations to find the value of $x$ . Let's use the first equation: $\newline$ $9x − 6y = −18$ $\newline$ Substitute $y = −3$ into the equation: $\newline$ $9x − 6(−3) = −18$
Solve for x: Solve for x: $\newline$ $9x + 18 = -18$ $\newline$ $9x = -18 - 18$ $\newline$ $9x = -36$ $\newline$ $x = -36 / 9$ $\newline$ $x = -4$
Final Values: We have found the values of $x$ and $y$ that solve the system of equations: $x = -4$ , $y = -3$