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Solve using elimination. $\newline$ $-x + 4y = -11$ $\newline$ $x - 2y = 5$ $\newline$ (_, _)

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Solve a system of equations using elimination

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Q. Solve using elimination.

\newline

-x + 4y = -11

\newline

x - 2y = 5

\newline

(_____, _____)

Write Equations: Write down the system of equations to be solved using elimination. $\newline$ $-x + 4y = -11$ $\newline$ $x - 2y = 5$
Add Equations: Add the two equations together to eliminate the variable $x$ . $(–x + 4y) + (x − 2y) = (–11) + (5)$ The $x$ terms cancel each other out, and we are left with: $4y - 2y = -11 + 5$
Simplify Equation: Simplify the equation by combining like terms. $\newline$ $4y - 2y = 2y$ $\newline$ $-11 + 5 = -6$ $\newline$ So, we have: $\newline$ $2y = -6$
Solve for y: Solve for y by dividing both sides of the equation by $2$ . $\newline$ $2y \div 2 = -6 \div 2$ $\newline$ $y = -3$
Substitute and Solve for $x$ : Substitute the value of $y$ back into one of the original equations to solve for $x$ . We can use the second equation $x − 2y = 5$ . $\newline$ $x - 2(-3) = 5$ $\newline$ $x + 6 = 5$
Solve for x: Solve for x by subtracting $6$ from both sides of the equation. $\newline$ $x + 6 - 6 = 5 - 6$ $\newline$ $x = -1$
Write Solution: Write down the solution to the system of equations as an ordered pair. $\newline$ The solution is $(x, y) = (-1, -3)$ .

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