Solve using elimination. –4x − 9y = 3 –5x − 9y = –3 (_____, _____)

Set Up Equations: First, we need to set up the equations to eliminate one of the variables. We have the following system of equations: –4x − 9y = 3 –5x − 9y = –3 To eliminate y, we can subtract the second equation from the first equation because the coefficients of y are the same but with opposite signs.Subtract Equations: Perform the subtraction of the two equations: (–4x − 9y) − (–5x − 9y) = 3 − (–3) This simplifies to: –4x + 5x − 9y + 9y = 3 + 3Simplify Result: Simplify the equation by combining like terms: x = 6 Now we have the value of x.Find Value of x: Next, we need to find the value of y. We can substitute x = 6 into one of the original equations. Let's use the first equation: –4x − 9y = 3 Substitute x with 6: –4(6) − 9y = 3Substitute x: Perform the multiplication and simplify the equation: –24 − 9y = 3 Now, we need to isolate y by adding 24 to both sides of the equation: –9y = 3 + 24Isolate y: Simplify the right side of the equation: –9y = 27 Now, divide both sides by -9 to solve for y: y = 27 / (–9)Calculate y: Calculate the value of y: y = –3 Now we have the value of y.

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Solve using elimination. $\newline$ $-4x - 9y = 3$ $\newline$ $-5x - 9y = -3$ $\newline$ (_, _)

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Grade 8

Solve a system of equations using elimination

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Q. Solve using elimination.

\newline

-4x - 9y = 3

\newline

-5x - 9y = -3

\newline

(_____, _____)

Set Up Equations: First, we need to set up the equations to eliminate one of the variables. We have the following system of equations: $\newline$ $-4x - 9y = 3$ $\newline$ $-5x - 9y = -3$ $\newline$ To eliminate $y$ , we can subtract the second equation from the first equation because the coefficients of $y$ are the same but with opposite signs.
Subtract Equations: Perform the subtraction of the two equations: $\newline$ $(-4x - 9y) - (-5x - 9y) = 3 - (-3)$ $\newline$ This simplifies to: $\newline$ $-4x + 5x - 9y + 9y = 3 + 3$
Simplify Result: Simplify the equation by combining like terms: $x = 6$ Now we have the value of $x$ .
Find Value of x: Next, we need to find the value of $y$ . We can substitute $x = 6$ into one of the original equations. Let's use the first equation: $\newline$ $–4x − 9y = 3$ $\newline$ Substitute $x$ with $6$ : $\newline$ $–4(6) − 9y = 3$
Substitute $x$ : Perform the multiplication and simplify the equation: $\newline$ $-24 - 9y = 3$ $\newline$ Now, we need to isolate $y$ by adding $24$ to both sides of the equation: $\newline$ $-9y = 3 + 24$
Isolate $y$ : Simplify the right side of the equation: $\newline$ $-9y = 27$ $\newline$ Now, divide both sides by $-9$ to solve for $y$ : $\newline$ $y = \frac{27}{(-9)}$
Calculate $y$ : Calculate the value of $y$ : $y = -3$ Now we have the value of $y$ .