Solve using elimination. –2x − 10y = 6 –2x − 8y = 8 (_____, _____)

Write Equations: Write down the system of equations. –2x − 10y = 6 –2x − 8y = 8Modify Second Equation: To use elimination, we want to eliminate one of the variables. We can do this by adding the two equations together. However, since both equations have the term –2x, we need to make one of them positive so that when we add the equations, the x terms cancel out. We can multiply the second equation by -1 to achieve this. Multiplying the second equation by -1 gives us: 2x + 8y = -8Add Equations: Now add the modified second equation to the first equation to eliminate the x variable. (–2x − 10y) + (2x + 8y) = 6 + (-8)Simplify Equation: Perform the addition to eliminate the x variable. –2x + 2x − 10y + 8y = 6 - 8 0x − 2y = -2Substitute y: Simplify the resulting equation to solve for y. −2y = -2 y = -2 / -2 y = 1Solve for x: Now that we have the value of y, we can substitute it back into one of the original equations to solve for x. Let's use the first equation: –2x − 10y = 6 Substitute y = 1: –2x − 10(1) = 6Solve for x. –2x − 10 = 6 Add 10 to both sides: –2x = 6 + 10 –2x = 16 Divide both sides by -2: x = 16 / -2 x = -8

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Solve using elimination. $\newline$ $-2x - 10y = 6$ $\newline$ $-2x - 8y = 8$ $\newline$ (_, _)

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Grade 8

Solve a system of equations using elimination

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Q. Solve using elimination.

\newline

-2x - 10y = 6

\newline

-2x - 8y = 8

\newline

(_____, _____)

Write Equations: Write down the system of equations. $\newline$ $-2x - 10y = 6$ $\newline$ $-2x - 8y = 8$
Modify Second Equation: To use elimination, we want to eliminate one of the variables. We can do this by adding the two equations together. However, since both equations have the term $–2x$ , we need to make one of them positive so that when we add the equations, the $x$ terms cancel out. We can multiply the second equation by $-1$ to achieve this. $\newline$ Multiplying the second equation by $-1$ gives us: $\newline$ $2x + 8y = -8$
Add Equations: Now add the modified second equation to the first equation to eliminate the $x$ variable. $\newline$ $(-2x - 10y) + (2x + 8y) = 6 + (-8)$
Simplify Equation: Perform the addition to eliminate the $x$ variable. $\,-2x + 2x - 10y + 8y = 6 - 8$ $\,0x - 2y = -2$
Substitute $y$ : Simplify the resulting equation to solve for $y$ . $\newline$ $−2y = -2$ $\newline$ $y = -2 / -2$ $\newline$ $y = 1$
Solve for x: Now that we have the value of $y$ , we can substitute it back into one of the original equations to solve for $x$ . Let's use the first equation: $\newline$ $–2x − 10y = 6$ $\newline$ Substitute $y = 1$ : $\newline$ $–2x − 10(1) = 6$
Solve for x: Now that we have the value of $y$ , we can substitute it back into one of the original equations to solve for $x$ . Let's use the first equation: $\newline$ $-2x - 10y = 6$ $\newline$ Substitute $y = 1$ : $\newline$ $-2x - 10(1) = 6$ Solve for $x$ . $\newline$ $-2x - 10 = 6$ $\newline$ Add $10$ to both sides: $\newline$ $-2x = 6 + 10$ $\newline$ $-2x = 16$ $\newline$ Divide both sides by $x$ $0$ : $\newline$ $x$ $1$ $\newline$ $x$ $2$