Solve using elimination. 2x − 2y = –2 2x − 8y = –20 (_____, _____)

Write Equations: First, let's write down the system of equations we need to solve: 2x − 2y = –2 2x − 8y = –20 We want to eliminate one of the variables by subtracting one equation from the other. Since the coefficients of x are the same, we can subtract the second equation from the first one to eliminate x.Subtract Equations: Perform the subtraction of the two equations: (2x − 2y) − (2x − 8y) = (–2) − (–20) This simplifies to: 2x − 2x − 2y + 8y = –2 + 20Simplify Result: Simplify the resulting equation: 0x + 6y = 18 Since 0x is 0, we can remove it from the equation: 6y = 18Solve for y: Now, we solve for y by dividing both sides of the equation by 6: 6y / 6 = 18 / 6 y = 3Substitute and Solve: With the value of y found, we can substitute it back into one of the original equations to find x. Let's use the first equation: 2x − 2(3) = –2 2x − 6 = –2Addition to Solve x: Add 6 to both sides of the equation to solve for x: 2x − 6 + 6 = –2 + 6 2x = 4Final Solution: Finally, divide both sides by 2 to find the value of x: 2x / 2 = 4 / 2 x = 2

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Solve using elimination. $\newline$ $2x - 2y = -2$ $\newline$ $2x - 8y = -20$ $\newline$ (_, _)

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Grade 8

Solve a system of equations using elimination

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Q. Solve using elimination.

\newline

2x - 2y = -2

\newline

2x - 8y = -20

\newline

(_____, _____)

Write Equations: First, let's write down the system of equations we need to solve: $\newline$ $2x − 2y = −2$ $\newline$ $2x − 8y = −20$ $\newline$ We want to eliminate one of the variables by subtracting one equation from the other. Since the coefficients of $x$ are the same, we can subtract the second equation from the first one to eliminate $x$ .
Subtract Equations: Perform the subtraction of the two equations: $\newline$ $(2x − 2y) − (2x − 8y) = (−2) − (−20)$ $\newline$ This simplifies to: $\newline$ $2x − 2x − 2y + 8y = −2 + 20$
Simplify Result: Simplify the resulting equation: $\newline$ $0x + 6y = 18$ $\newline$ Since $0x$ is $0$ , we can remove it from the equation: $\newline$ $6y = 18$
Solve for y: Now, we solve for $y$ by dividing both sides of the equation by $6$ : $\frac{6y}{6} = \frac{18}{6}$ $y = 3$
Substitute and Solve: With the value of $y$ found, we can substitute it back into one of the original equations to find $x$ . Let's use the first equation: $\newline$ $2x − 2(3) = −2$ $\newline$ $2x − 6 = −2$
Addition to Solve $x$ : Add $6$ to both sides of the equation to solve for $x$ : $2x − 6 + 6 = −2 + 6$ $2x = 4$
Final Solution: Finally, divide both sides by $2$ to find the value of $x$ : $\frac{2x}{2} = \frac{4}{2}$ $x = 2$