Solve using elimination. 10x − 5y = 5 9x − 5y = 9 (_____, _____)

Write Equations: Write down the system of equations to be solved using elimination. 10x − 5y = 5 9x − 5y = 9Eliminate y: Subtract the second equation from the first equation to eliminate the y variable. (10x − 5y) − (9x − 5y) = 5 − 9Find x: Perform the subtraction to find the value of x. 10x − 9x = 5 − 9 x = −4Substitute x: Substitute the value of x back into one of the original equations to solve for y. Using the first equation: 10x − 5y = 5 10(−4) − 5y = 5 −40 − 5y = 5Isolate y: Add 40 to both sides of the equation to isolate the term containing y. −40 + 40 − 5y = 5 + 40 −5y = 45Solve for y: Divide both sides by -5 to solve for y. −5y / -5 = 45 / -5 y = −9

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Solve using elimination. $\newline$ $10x - 5y = 5$ $\newline$ $9x - 5y = 9$ $\newline$ (_, _)

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Grade 8

Solve a system of equations using elimination

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Q. Solve using elimination.

\newline

10x - 5y = 5

\newline

9x - 5y = 9

\newline

(_____, _____)

Write Equations: Write down the system of equations to be solved using elimination. $\newline$ $10x − 5y = 5$ $\newline$ $9x − 5y = 9$
Eliminate y: Subtract the second equation from the first equation to eliminate the $y$ variable. $\newline$ $(10x − 5y) − (9x − 5y) = 5 − 9$
Find $x$ : Perform the subtraction to find the value of $x$ . $10x − 9x = 5 − 9$ $x = −4$
Substitute $x$ : Substitute the value of $x$ back into one of the original equations to solve for $y$ . $\newline$ Using the first equation: $10x − 5y = 5$ $\newline$ $10(−4) − 5y = 5$ $\newline$ $−40 − 5y = 5$
Isolate y: Add $40$ to both sides of the equation to isolate the term containing $y$ . $\newline$ $-40 + 40 - 5y = 5 + 40$ $\newline$ $-5y = 45$
Solve for y: Divide both sides by $-5$ to solve for y. $\newline$ $\frac{-5y}{-5} = \frac{45}{-5}$ $\newline$ $y = -9$