Solve using elimination. 5x − 8y = 3 5x + 10y = –15 (_____, _____)

Set Up Equations: First, we need to set up the equations to eliminate one of the variables. We can do this by subtracting one equation from the other since the coefficients of x are the same in both equations. 5x − 8y = 3 5x + 10y = –15 Subtract the second equation from the first one to eliminate the x variable. (5x − 8y) - (5x + 10y) = 3 - (–15)Subtract Equations: Now, perform the subtraction: 5x - 5x - 8y - 10y = 3 + 15 This simplifies to: 0x - 18y = 18 Since 0x is 0, we can ignore it, and we are left with: -18y = 18Perform Subtraction: Next, we solve for y by dividing both sides of the equation by -18: -18y / -18 = 18 / -18 y = -1Solve for y: 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: 5x − 8y = 3 5x − 8(-1) = 3 5x + 8 = 3Substitute Back: Subtract 8 from both sides to solve for x: 5x + 8 - 8 = 3 - 8 5x = -5Solve for x: Finally, divide both sides by 5 to find the value of x: 5x / 5 = -5 / 5 x = -1

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Solve using elimination. $\newline$ $5x - 8y = 3$ $\newline$ $5x + 10y = -15$ $\newline$ (_, _)

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Grade 8

Solve a system of equations using elimination

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Q. Solve using elimination.

\newline

5x - 8y = 3

\newline

5x + 10y = -15

\newline

(_____, _____)

Set Up Equations: First, we need to set up the equations to eliminate one of the variables. We can do this by subtracting one equation from the other since the coefficients of $x$ are the same in both equations. $5x − 8y = 3$ $5x + 10y = −15$ Subtract the second equation from the first one to eliminate the $x$ variable. $(5x − 8y) - (5x + 10y) = 3 - (−15)$
Subtract Equations: Now, perform the subtraction: $\newline$ $5x - 5x - 8y - 10y = 3 + 15$ $\newline$ This simplifies to: $\newline$ $0x - 18y = 18$ $\newline$ Since $0x$ is $0$ , we can ignore it, and we are left with: $\newline$ $-18y = 18$
Perform Subtraction: Next, we solve for $y$ by dividing both sides of the equation by $-18$ : $\frac{-18y}{-18} = \frac{18}{-18}$ $y = -1$
Solve for y: 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: $\newline$ $5x − 8y = 3$ $\newline$ $5x − 8(-1) = 3$ $\newline$ $5x + 8 = 3$
Substitute Back: Subtract $8$ from both sides to solve for $x$ : $\newline$ $5x + 8 - 8 = 3 - 8$ $\newline$ $5x = -5$
Solve for x: Finally, divide both sides by $5$ to find the value of x: $\newline$ $\frac{5x}{5} = \frac{-5}{5}$ $\newline$ $x = -1$