Solve using elimination. –10x − 2y = 8 –10x − y = –1 (_____, _____)

Write Equations: Write down the system of equations to be solved. –10x − 2y = 8 –10x − y = –1Elimination Step: In order to use elimination, we need to eliminate one of the variables. We can do this by subtracting the second equation from the first equation. Subtracting the second equation from the first, we get: (–10x − 2y) − (–10x − y) = 8 − (–1)Subtraction Operation: Perform the subtraction operation on the left side of the equation. –10x + 10x − 2y + y = 8 + 1 This simplifies to: −2y + y = 9Combine Like Terms: Combine like terms on the left side of the equation. −2y + y = −y So, we have: −y = 9Solve for y: Solve for y by dividing both sides of the equation by -1. −y / -1 = 9 / -1 y = −9Substitute and Simplify: Now that we have the value of y, we can substitute it back into one of the original equations to solve for x. Let's use the second equation: –10x − y = –1 Substitute y = −9 into the equation: –10x − (−9) = –1Solve for x: Simplify the equation by adding 9 to both sides. –10x + 9 = –1 –10x = –1 − 9 –10x = –10Final Solution: Solve for x by dividing both sides of the equation by -10. –10x / -10 = –10 / -10 x = 1We have found the values of x and y that solve the system of equations. x = 1, y = −9

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Solve using elimination. $\newline$ $-10x - 2y = 8$ $\newline$ $-10x - y = -1$ $\newline$ (_, _)

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Grade 8

Solve a system of equations using elimination

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Q. Solve using elimination.

\newline

-10x - 2y = 8

\newline

-10x - y = -1

\newline

(_____, _____)

Write Equations: Write down the system of equations to be solved. $\newline$ $-10x - 2y = 8$ $\newline$ $-10x - y = -1$
Elimination Step: In order to use elimination, we need to eliminate one of the variables. We can do this by subtracting the second equation from the first equation. $\newline$ Subtracting the second equation from the first, we get: $\newline$ $(–10x − 2y) − (–10x − y) = 8 − (–1)$
Subtraction Operation: Perform the subtraction operation on the left side of the equation. $\newline$ $-10x + 10x - 2y + y = 8 + 1$ $\newline$ This simplifies to: $\newline$ $-2y + y = 9$
Combine Like Terms: Combine like terms on the left side of the equation. $\newline$ $-2y + y = -y$ $\newline$ So, we have: $\newline$ $-y = 9$
Solve for y: Solve for y by dividing both sides of the equation by $-1$ . $\newline$ $\frac{-y}{-1} = \frac{9}{-1}$ $\newline$ $y = -9$
Substitute and Simplify: Now that we have the value of $y$ , we can substitute it back into one of the original equations to solve for $x$ . Let's use the second equation: $\newline$ $–10x − y = –1$ $\newline$ Substitute $y = −9$ into the equation: $\newline$ $–10x − (−9) = –1$
Solve for x: Simplify the equation by adding $9$ to both sides. $\newline$ $-10x + 9 = -1$ $\newline$ $-10x = -1 - 9$ $\newline$ $-10x = -10$
Final Solution: Solve for $x$ by dividing both sides of the equation by $-10$ . $\frac{-10x}{-10} = \frac{-10}{-10}$ $x = 1$
Final Solution: Solve for $x$ by dividing both sides of the equation by $-10$ . $\frac{-10x}{-10} = \frac{-10}{-10}$ $x = 1$ We have found the values of $x$ and $y$ that solve the system of equations. $x = 1, y = -9$