Solve using elimination. 10x − 8y = –10 9x − 8y = –17 (_____, _____)

Set up equations: First, we need to set up the equations to eliminate one of the variables. We can do this by subtracting the second equation from the first equation since the coefficients of y are the same but with opposite signs. 10x − 8y = –10 -(9x − 8y = –17)Subtract to eliminate variable: Perform the subtraction of the two equations to eliminate the y variable. (10x − 8y) - (9x − 8y) = (–10) - (–17)Simplify resulting equation: Simplify the resulting equation. 10x - 9x = –10 + 17Calculate x value: Calculate the value of x. x = 7Substitute x to solve y: Now that we have the value of x, we can substitute it back into one of the original equations to solve for y. Let's use the first equation: 10x − 8y = –10 10(7) − 8y = –10Perform multiplication: Perform the multiplication to simplify the equation. 70 − 8y = –10Isolate term with y: Subtract 70 from both sides to isolate the term with y. −8y = –10 − 70Divide to solve for y: Simplify the right side of the equation. −8y = –80Calculate y value: Divide both sides by -8 to solve for y. y = –80 / -8Calculate the value of y. y = 10

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Solve using elimination. $\newline$ $10x - 8y = -10$ $\newline$ $9x - 8y = -17$ $\newline$ (_, _)

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Grade 8

Solve a system of equations using elimination

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Q. Solve using elimination.

\newline

10x - 8y = -10

\newline

9x - 8y = -17

\newline

(_____, _____)

Set up equations: First, we need to set up the equations to eliminate one of the variables. We can do this by subtracting the second equation from the first equation since the coefficients of $y$ are the same but with opposite signs. $10x − 8y = −10$ $-(9x − 8y = −17)$
Subtract to eliminate variable: Perform the subtraction of the two equations to eliminate the $y$ variable. $\newline$ $(10x − 8y) - (9x − 8y) = (−10) - (−17)$
Simplify resulting equation: Simplify the resulting equation. $10x - 9x = -10 + 17$
Calculate x value: Calculate the value of x. $\newline$ $x = 7$
Substitute $x$ to solve $y$ : Now that we have the value of $x$ , we can substitute it back into one of the original equations to solve for $y$ . Let's use the first equation: $\newline$ $10x − 8y = −10$ $\newline$ $10(7) − 8y = −10$
Perform multiplication: Perform the multiplication to simplify the equation. $70 - 8y = -10$
Isolate term with y: Subtract $70$ from both sides to isolate the term with y. $\newline$ $-8y = -10 - 70$
Divide to solve for y: Simplify the right side of the equation. $\newline$ $-8y = -80$
Calculate y value: Divide both sides by $-8$ to solve for y. $\newline$ $y = \frac{-80}{-8}$
Calculate y value: Divide both sides by $-8$ to solve for y. $\newline$ y = $–80 / -8$ Calculate the value of y. $\newline$ y = $10$