Solve using elimination. x + 2y = –10 3x + 2y = 6 (_____, _____)

Set up equations: First, we need to set up the equations to eliminate one of the variables. We can do this by subtracting the second equation from the first equation since they both have the same coefficient for y. x + 2y = –10 3x + 2y = 6 Subtract the first equation from the second equation to eliminate y. (3x + 2y) - (x + 2y) = 6 - (–10)Subtract to eliminate y: Now, perform the subtraction: 3x + 2y - x - 2y = 6 + 10 2x = 16Perform subtraction: Next, solve for x by dividing both sides of the equation by 2: 2x / 2 = 16 / 2 x = 8Solve for x: Now that we have the value of x, we can substitute it back into one of the original equations to solve for y. Let's use the first equation: x + 2y = –10 8 + 2y = –10Substitute x into equation: Subtract 8 from both sides to solve for 2y: 2y = –10 - 8 2y = –18Solve for 2y: Finally, divide both sides by 2 to find the value of y: 2y / 2 = –18 / 2 y = –9

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Solve using elimination. $\newline$ $x + 2y = -10$ $\newline$ $3x + 2y = 6$ $\newline$ (_, _)

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Grade 8

Solve a system of equations using elimination

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Q. Solve using elimination.

\newline

x + 2y = -10

\newline

3x + 2y = 6

\newline

(_____, _____)

Set up equations: First, we need to set up the equations to eliminate one of the variables. We can do this by subtracting the second equation from the first equation since they both have the same coefficient for $y$ . $x + 2y = -10$ $3x + 2y = 6$ Subtract the first equation from the second equation to eliminate $y$ . $(3x + 2y) - (x + 2y) = 6 - (-10)$
Subtract to eliminate $y$ : Now, perform the subtraction: $\newline$ $3x + 2y - x - 2y = 6 + 10$ $\newline$ $2x = 16$
Perform subtraction: Next, solve for $x$ by dividing both sides of the equation by $2$ : $\frac{2x}{2} = \frac{16}{2}$ $x = 8$
Solve for x: Now that we have the value of $x$ , we can substitute it back into one of the original equations to solve for $y$ . Let's use the first equation: $\newline$ $x + 2y = -10$ $\newline$ $8 + 2y = -10$
Substitute $x$ into equation: Subtract $8$ from both sides to solve for $2y$ : $2y = -10 - 8$ $2y = -18$
Solve for $2y$ : Finally, divide both sides by $2$ to find the value of $y$ : $\frac{2y}{2} = \frac{-18}{2}$ $y = -9$