Solve using elimination. –5x − y = –1 5x − y = 19 (_____, _____)

Write Equations: Write down the system of equations. –5x − y = –1 5x − y = 19Add and Eliminate x: Add the two equations together to eliminate the x variable. (–5x − y) + (5x − y) = (–1) + (19) The x terms cancel each other out, and we are left with: –y − y = 18Combine Like Terms: Combine like terms. –2y = 18Solve for y: Solve for y by dividing both sides by –2. y = 18 / (–2) y = –9Substitute and Solve for x: Substitute y = –9 into one of the original equations to solve for x. We can use the first equation: –5x − (–9) = –1 –5x + 9 = –1Isolate x Term: Subtract 9 from both sides to isolate the term with x. –5x + 9 − 9 = –1 − 9 –5x = –10Solve for x: Divide both sides by –5 to solve for x. x = –10 / (–5) x = 2Write Ordered Pair: Write the solution as an ordered pair. The solution to the system of equations is (x, y) = (2, –9).

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Solve using elimination. $\newline$ $-5x - y = -1$ $\newline$ $5x - y = 19$ $\newline$ (_, _)

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Grade 8

Solve a system of equations using elimination

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Q. Solve using elimination.

\newline

-5x - y = -1

\newline

5x - y = 19

\newline

(_____, _____)

Write Equations: Write down the system of equations. $\newline$ $-5x - y = -1$ $\newline$ $5x - y = 19$
Add and Eliminate $x$ : Add the two equations together to eliminate the $x$ variable. $\newline$ $(-5x - y) + (5x - y) = (-1) + (19)$ $\newline$ The $x$ terms cancel each other out, and we are left with: $\newline$ $-y - y = 18$
Combine Like Terms: Combine like terms. $\newline$ $-2y = 18$
Solve for y: Solve for y by dividing both sides by $–2$ . $\newline$ $y = \frac{18}{(–2)}$ $\newline$ $y = –9$
Substitute and Solve for x: Substitute $y = -9$ into one of the original equations to solve for $x$ . We can use the first equation: $\newline$ $-5x - (-9) = -1$ $\newline$ $-5x + 9 = -1$
Isolate x Term: Subtract $9$ from both sides to isolate the term with $x$ .
$-5x + 9 - 9 = -1 - 9$
$-5x = -10$
Solve for x: Divide both sides by $–5$ to solve for x. $\newline$ $x = \frac{–10}{(–5)}$ $\newline$ $x = 2$
Write Ordered Pair: Write the solution as an ordered pair. $\newline$ The solution to the system of equations is $(x, y) = (2, -9)$ .