Solve using elimination. –8x + 9y = 12 –9x + 9y = 9 (_____, _____)

Write Equations: Write down the system of equations. –8x + 9y = 12 –9x + 9y = 9Elimination Method: To use elimination, we want to eliminate one of the variables by adding or subtracting the equations. Since the coefficients of y are the same, we can subtract the second equation from the first to eliminate y. Subtract the second equation from the first: (–8x + 9y) - (–9x + 9y) = 12 - 9Subtract Equations: Perform the subtraction. –8x + 9y + 9x - 9y = 12 - 9Simplify Result: Simplify the equation. x = 3Substitute x Value: Now that we have the value of x, we can substitute it back into one of the original equations to find the value of y. Let's use the first equation: –8x + 9y = 12 Substitute x = 3 into the equation: –8(3) + 9y = 12Solve for y: Perform the multiplication and solve for y. –24 + 9y = 12Isolate y Term: Add 24 to both sides of the equation to isolate the term with y. 9y = 12 + 24Divide to Solve y: Perform the addition. 9y = 36Calculate Final y Value: Divide both sides by 9 to solve for y. y = 36 / 9Calculate the value of y. y = 4

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Solve using elimination. $\newline$ $-8x + 9y = 12$ $\newline$ $-9x + 9y = 9$ $\newline$ (_, _)

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Grade 8

Solve a system of equations using elimination

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Q. Solve using elimination.

\newline

-8x + 9y = 12

\newline

-9x + 9y = 9

\newline

(_____, _____)

Write Equations: Write down the system of equations. $\newline$ $-8x + 9y = 12$ $\newline$ $-9x + 9y = 9$
Elimination Method: To use elimination, we want to eliminate one of the variables by adding or subtracting the equations. Since the coefficients of $y$ are the same, we can subtract the second equation from the first to eliminate $y$ . $\newline$ Subtract the second equation from the first: $\newline$ $(–8x + 9y) - (–9x + 9y) = 12 - 9$
Subtract Equations: Perform the subtraction. $\newline$ $-8x + 9y + 9x - 9y = 12 - 9$
Simplify Result: Simplify the equation. $\newline$ $x = 3$
Substitute $x$ Value: Now that we have the value of $x$ , we can substitute it back into one of the original equations to find the value of $y$ . Let's use the first equation: $\newline$ $–8x + 9y = 12$ $\newline$ Substitute $x = 3$ into the equation: $\newline$ $–8(3) + 9y = 12$
Solve for y: Perform the multiplication and solve for y. $-24 + 9y = 12$
Isolate y Term: Add $24$ to both sides of the equation to isolate the term with $y$ . $\newline$ $9y = 12 + 24$
Divide to Solve $y$ : Perform the addition. $9y = 36$
Calculate Final y Value: Divide both sides by $9$ to solve for y. $\newline$ $y = \frac{36}{9}$
Calculate Final y Value: Divide both sides by $9$ to solve for y. $\newline$ y = $\frac{36}{9}$ Calculate the value of y. $\newline$ y = $4$