Solve using elimination. 4x − 7y = –5 4x − 9y = 5 (_____, _____)

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 − 7y = –5 4x − 9y = 5Subtract Equations: To eliminate the variable x, we can subtract the second equation from the first equation: (4x − 7y) − (4x − 9y) = (–5) − (5)Perform Subtraction: Perform the subtraction: 4x - 4x − 7y + 9y = –5 − 5Simplify Equation: Simplify the equation: 0x + 2y = –10 This simplifies to: 2y = –10Solve for y: Divide both sides by 2 to solve for y: y = –10 / 2 y = –5Substitute Back: Now that we have the value of y, we can substitute it back into one of the original equations to solve for x. We'll use the first equation: 4x − 7(–5) = –5Multiply 7: Multiply 7 by –5: 4x + 35 = –5Subtract 35: Subtract 35 from both sides to solve for x: 4x = –5 − 35 4x = –40Divide by 4: Divide both sides by 4 to find the value of x: x = –40 / 4 x = –10

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Solve using elimination. $\newline$ $4x - 7y = -5$ $\newline$ $4x - 9y = 5$ $\newline$ (_, _)

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Grade 8

Solve a system of equations using elimination

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Q. Solve using elimination.

\newline

4x - 7y = -5

\newline

4x - 9y = 5

\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: $\newline$ $4x − 7y = −5$ $\newline$ $4x − 9y = 5$
Subtract Equations: To eliminate the variable $x$ , we can subtract the second equation from the first equation: $(4x − 7y) − (4x − 9y) = (−5) − (5)$
Perform Subtraction: Perform the subtraction: $4x - 4x - 7y + 9y = -5 - 5$
Simplify Equation: Simplify the equation: $\newline$ $0x + 2y = -10$ $\newline$ This simplifies to: $\newline$ $2y = -10$
Solve for y: Divide both sides by $2$ to solve for y: $\newline$ y = $-10 / 2$ $\newline$ y = $-5$
Substitute Back: Now that we have the value of $y$ , we can substitute it back into one of the original equations to solve for $x$ . We'll use the first equation: $\newline$ $4x − 7(–5) = –5$
Multiply $7$ : Multiply $7$ by $-5$ : $4x + 35 = -5$
Subtract $35$ : Subtract $35$ from both sides to solve for $x$ : $4x = -5 - 35$ $4x = -40$
Divide by $4$ : Divide both sides by $4$ to find the value of x: $\newline$ $x = \frac{-40}{4}$ $\newline$ $x = -10$