Solve the system by substitution. {:[-2x-2y=-32],[-9y=x]:}

Identify Equation for Substitution: Identify the easier equation to use for substitution. The second equation, -9y = x, is already solved for x, making it the easiest to use for substitution.Substitute x into First Equation: Substitute x from the second equation into the first equation. The first equation is -2x - 2y = -32. Substituting x with -9y from the second equation gives us -2(-9y) - 2y = -32.Simplify and Solve for y: Simplify the equation and solve for y. 18y - 2y = -32 16y = -32 Divide both sides by 16 to find y. y = -32 / 16 y = -2Substitute y into Second Equation: Substitute y back into the second equation to find x. The second equation is -9y = x. Substituting y with -2 gives us -9(-2) = x. x = 18Write Solution as Ordered Pair: Write the solution as an ordered pair (x, y). The solution is (18, -2).

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Solve the system by substitution.

{:[-2x-2y=-32],[-9y=x]:}

Solve the system by substitution. $\newline$ $\begin{aligned} -2 x-2 y & =-32 \\ -9 y & =x \end{aligned}$

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Algebra 2

Solve a system of equations in three variables using substitution

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Q. Solve the system by substitution.

\newline

\begin{aligned} -2 x-2 y & =-32 \\ -9 y & =x \end{aligned}

Identify Equation for Substitution: Identify the easier equation to use for substitution. $\newline$ The second equation, $-9y = x$ , is already solved for $x$ , making it the easiest to use for substitution.
Substitute $x$ into First Equation: Substitute $x$ from the second equation into the first equation. $\newline$ The first equation is $-2x - 2y = -32$ . Substituting $x$ with $-9y$ from the second equation gives us $-2(-9y) - 2y = -32$ .
Simplify and Solve for $y$ : Simplify the equation and solve for $y$ .
$18y - 2y = -32$
$16y = -32$
Divide both sides by $16$ to find $y$ .
$y = -32 / 16$
$y = -2$
Substitute $y$ into Second Equation: Substitute $y$ back into the second equation to find $x$ . The second equation is $-9y = x$ . Substituting $y$ with $-2$ gives us $-9(-2) = x$ . $x = 18$
Write Solution as Ordered Pair: Write the solution as an ordered pair $(x, y)$ . The solution is $(18, -2)$ .