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Solve the system by substitution.

{:[-6x-5y=-8],[y=-2x]:}

(◻,◻)

Solve the system by substitution. $\newline$ $\begin{aligned} -6 x-5 y & =-8 \\ y & =-2 x \end{aligned}$ $\newline$ $(\square, \square)$

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Identify independent and dependent variables: word problems

Full solution

Q. Solve the system by substitution.

\newline

\begin{aligned} -6 x-5 y & =-8 \\ y & =-2 x \end{aligned}

\newline

(\square, \square)

Identify Equation: Identify the equation that can be easily substituted. $\newline$ The second equation $y = -2x$ is already solved for $y$ , which makes it easy to substitute into the first equation.
Substitute $y$ : Substitute $y = -2x$ into the first equation. $\newline$ The first equation is $-6x - 5y = -8$ . We can substitute $y$ with $-2x$ to get $-6x - 5(-2x) = -8$ .
Simplify and Solve: Simplify and solve for $x$ . Simplifying the equation gives us $-6x + 10x = -8$ , which simplifies further to $4x = -8$ . Dividing both sides by $4$ gives us $x = -8 / 4$ , which simplifies to $x = -2$ .
Substitute $x$ : Substitute $x = -2$ back into the second equation to solve for $y$ . Substituting $x$ into $y = -2x$ gives us $y = -2(-2)$ , which simplifies to $y = 4$ .
Write Solution: Write the solution as an ordered pair. $\newline$ The solution to the system of equations is $(x, y) = (-2, 4)$ .

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