Solve using elimination. –2x − 2y = 10 4x − 2y = 4 (_____, _____)

Write Equations: First, let's write down the system of equations: –2x − 2y = 10 4x − 2y = 4 To use elimination, we want to add or subtract the equations to eliminate one of the variables. In this case, we can add the two equations together to eliminate the y variable.Add Equations: Now, let's add the two equations: (–2x − 2y) + (4x − 2y) = 10 + 4 This simplifies to: –2x + 4x − 2y − 2y = 14Combine Terms: Combining like terms gives us: 2x = 14Solve for x: Next, we solve for x by dividing both sides of the equation by 2: 2x / 2 = 14 / 2 This gives us: x = 7Substitute x: Now that we have the value of x, we can substitute it back into one of the original equations to find the value of y. Let's use the first equation: –2x − 2y = 10 Substituting x = 7, we get: –2(7) − 2y = 10Simplify Equation: Simplifying the equation, we have: –14 − 2y = 10Isolate y Term: Now, we add 14 to both sides to isolate the term with y: –14 + 14 − 2y = 10 + 14 This simplifies to: −2y = 24Solve for y: Finally, we divide both sides by -2 to solve for y: −2y / -2 = 24 / -2 This gives us: y = -12

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Solve using elimination. $\newline$ $-2x - 2y = 10$ $\newline$ $4x - 2y = 4$ $\newline$ (_, _)

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Grade 8

Solve a system of equations using elimination

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Q. Solve using elimination.

\newline

-2x - 2y = 10

\newline

4x - 2y = 4

\newline

(_____, _____)

Write Equations: First, let's write down the system of equations: $\newline$ $-2x - 2y = 10$ $\newline$ $4x - 2y = 4$ $\newline$ To use elimination, we want to add or subtract the equations to eliminate one of the variables. In this case, we can add the two equations together to eliminate the $y$ variable.
Add Equations: Now, let's add the two equations: $\newline$ $(-2x - 2y) + (4x - 2y) = 10 + 4$ $\newline$ This simplifies to: $\newline$ $-2x + 4x - 2y - 2y = 14$
Combine Terms: Combining like terms gives us: $2x = 14$
Solve for x: Next, we solve for x by dividing both sides of the equation by $2$ : $\newline$ $\frac{2x}{2} = \frac{14}{2}$ $\newline$ This gives us: $\newline$ $x = 7$
Substitute $x$ : Now that we have the value of $x$ , we can substitute it back into one of the original equations to find the value of $y$ . Let's use the first equation: $\newline$ $–2x − 2y = 10$ $\newline$ Substituting $x = 7$ , we get: $\newline$ $–2(7) − 2y = 10$
Simplify Equation: Simplifying the equation, we have: $-14 - 2y = 10$
Isolate y Term: Now, we add $14$ to both sides to isolate the term with $y$ : $\newline$ $-14 + 14 - 2y = 10 + 14$ $\newline$ This simplifies to: $\newline$ $-2y = 24$
Solve for y: Finally, we divide both sides by $-2$ to solve for $y$ : $\frac{-2y}{-2} = \frac{24}{-2}$ This gives us: $y = -12$