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Solve using elimination. $\newline$ $-x - 4y = 17$ $\newline$ $-x + 2y = -19$ $\newline$ (_, _)

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Solve a system of equations using elimination

Full solution

Q. Solve using elimination.

\newline

-x - 4y = 17

\newline

-x + 2y = -19

\newline

(_____, _____)

Write Equations: Write down the system of equations. $\newline$ $-x - 4y = 17$ $\newline$ $-x + 2y = -19$ $\newline$ We need to eliminate one variable to solve for the other.
Add Equations: Add the two equations together to eliminate the variable $x$ .( $-x - 4y$ + $-x + 2y$ = $17$ + $-19$ \)The $x$ terms cancel each other out, and we are left with: $-4$ y + $2$ y = $-2$ \)
Combine Terms: Combine like terms to simplify the equation. $\newline$ $-4y + 2y = -2y$ $\newline$ $-2y = -2$
Solve for y: Solve for y by dividing both sides of the equation by $-2$ . $\newline$ $\frac{-2y}{(-2)} = \frac{-2}{(-2)}$ $\newline$ $y = 1$ $\newline$ We have found the value of $y$ .
Substitute and Solve for $x$ : Substitute the value of $y$ back into one of the original equations to solve for $x$ . Using the second equation: $–x + 2y = –19$ Substitute $y = 1$ : $–x + 2(1) = –19$ $–x + 2 = –19$
Isolate $x$ : Solve for $x$ by isolating the variable. $\newline$ Subtract $2$ from both sides: $-x = -19 - 2$ $\newline$ $-x = -21$ $\newline$ Multiply both sides by $-1$ to get the positive value of $x$ : $x = 21$ $\newline$ We have found the value of $x$ .
Write Ordered Pair: Write the solution as an ordered pair $(x, y)$ . The solution to the system of equations is $(21, 1)$ .

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