Solve the system by substitution. {:[2x+5y=-2],[x=-4y-4]:}

Identify Equation for Substitution: Identify the equation that can be used for substitution. In the given system of equations, the second equation x = -4y - 4 is already solved for x, which makes it a good candidate for substitution.Substitute x into First Equation: Substitute the expression for x from the second equation into the first equation. Replace x in 2x + 5y = -2 with the expression from x = -4y - 4. 2(-4y - 4) + 5y = -2Distribute and Combine Terms: Distribute and combine like terms. 2(-4y) - 2(4) + 5y = -2 -8y - 8 + 5y = -2 Combine like terms: -8y + 5y = -3y -3y - 8 = -2Isolate y: Isolate y by adding 8 to both sides of the equation. -3y - 8 + 8 = -2 + 8 -3y = 6Solve for y: Solve for y by dividing both sides by -3. -3y / -3 = 6 / -3 y = -2Substitute y into Second Equation: Substitute the value of y back into the second equation to solve for x. x = -4y - 4 x = -4(-2) - 4 x = 8 - 4 x = 4Write Solution as Ordered Pair: Write the solution as an ordered pair (x, y). The solution to the system of equations is (4, -2).

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Solve the system by substitution.

{:[2x+5y=-2],[x=-4y-4]:}

Solve the system by substitution. $\newline$ $\begin{aligned} 2 x+5 y & =-2 \\ x & =-4 y-4 \end{aligned}$

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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+5 y & =-2 \\ x & =-4 y-4 \end{aligned}

Identify Equation for Substitution: Identify the equation that can be used for substitution. $\newline$ In the given system of equations, the second equation $x = -4y - 4$ is already solved for $x$ , which makes it a good candidate for substitution.
Substitute $x$ into First Equation: Substitute the expression for $x$ from the second equation into the first equation. $\newline$ Replace $x$ in $2x + 5y = -2$ with the expression from $x = -4y - 4$ . $\newline$ $2(-4y - 4) + 5y = -2$
Distribute and Combine Terms: Distribute and combine like terms. $\newline$ $2(-4y) - 2(4) + 5y = -2$ $\newline$ $-8y - 8 + 5y = -2$ $\newline$ Combine like terms: $-8y + 5y = -3y$ $\newline$ $-3y - 8 = -2$
Isolate y: Isolate y by adding $8$ to both sides of the equation. $\newline$ $-3y - 8 + 8 = -2 + 8$ $\newline$ $-3y = 6$
Solve for y: Solve for y by dividing both sides by -3＂).$\newline\$-3y / -3 = 6 / -3$$\newline$$y = -2$
Substitute $y$ into Second Equation: Substitute the value of $y$ back into the second equation to solve for $x$.\[x = -4y - 4\]\[x = -4(-2) - 4\]\[x = 8 - 4\]\[x = 4\]
Write Solution as Ordered Pair: Write the solution as an ordered pair $(x, y)$. The solution to the system of equations is $(4, -2)$.