Solve using elimination. –x − 2y = –9 –4x − 2y = 18 (_____, _____)

Write Equations: Write down the system of equations. –x − 2y = –9 –4x − 2y = 18 We want to eliminate one of the variables by adding or subtracting the equations. Since the coefficients of y are the same but with opposite signs, we can add the two equations to eliminate y.Add Equations: Add the two equations together. (–x − 2y) + (–4x − 2y) = (–9) + (18) When we add the equations, the y terms cancel out: –x + (–4x) = –9 + 18 –5x = 9 Now we can solve for x.Solve for x: Divide both sides by –5 to solve for x. –5x / –5 = 9 / –5 x = –9 / 5 x = –1.8 We have found the value of x.Substitute x: Substitute the value of x back into one of the original equations to solve for y. We can use the first equation: –x − 2y = –9 Substitute x = –1.8 into the equation: –(–1.8) − 2y = –9 1.8 − 2y = –9 Now we need to solve for y.Isolate y: Subtract 1.8 from both sides to isolate the term with y. 1.8 − 2y − 1.8 = –9 − 1.8 −2y = –10.8 Now we can solve for y by dividing both sides by –2.Solve for y: Divide both sides by –2 to solve for y. −2y / –2 = –10.8 / –2 y = 5.4 We have found the value of y.

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Solve using elimination. $\newline$ $-x - 2y = -9$ $\newline$ $-4x - 2y = 18$ $\newline$ (_, _)

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Grade 8

Solve a system of equations using elimination

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Q. Solve using elimination.

\newline

-x - 2y = -9

\newline

-4x - 2y = 18

\newline

(_____, _____)

Write Equations: Write down the system of equations. $\newline$ $-x - 2y = -9$ $\newline$ $-4x - 2y = 18$ $\newline$ We want to eliminate one of the variables by adding or subtracting the equations. Since the coefficients of $y$ are the same but with opposite signs, we can add the two equations to eliminate $y$ .
Add Equations: Add the two equations together. $\newline$ $(-x - 2y) + (-4x - 2y) = (-9) + (18)$ $\newline$ When we add the equations, the y terms cancel out: $\newline$ $-x + (-4x) = -9 + 18$ $\newline$ $-5x = 9$ $\newline$ Now we can solve for x.
Solve for x: Divide both sides by extendash{} $5$ to solve for x. $\newline$ extendash{} $5$ x / extendash{} $5$ = $9$ / extendash{} $5$ $\newline$ $x = extendash{}9 / 5$ $\newline$ $x = extendash{}1.8$ $\newline$ We have found the value of $x$ .
Substitute $x$ : Substitute the value of $x$ back into one of the original equations to solve for $y$ . We can use the first equation: $–x − 2y = –9$ Substitute $x = –1.8$ into the equation: $–(–1.8) − 2y = –9$ $1.8 − 2y = –9$ Now we need to solve for $y$ .
Isolate y: Subtract $1.8$ from both sides to isolate the term with $y$ . $\newline$ $1.8 - 2y - 1.8 = -9 - 1.8$ $\newline$ $-2y = -10.8$ $\newline$ Now we can solve for $y$ by dividing both sides by $-2$ .
Solve for y: Divide both sides by $–2$ to solve for y. $\frac{-2y}{-2} = \frac{-10.8}{-2}$ $y = 5.4$ We have found the value of $y$ .