Solve the system by substitution. {:[-4x+4y=-40],[y=3x-4]:}

Substitute y with 3x - 4: Substitute y with 3x - 4 in the first equation. The first equation is -4x + 4y = -40 and the second equation gives us y = 3x - 4. We will substitute y in the first equation with the expression from the second equation. -4x + 4(3x - 4) = -40Distribute and simplify: Distribute 4 into the parentheses and simplify. -4x + 12x - 16 = -40 Combine like terms. 8x - 16 = -40Combine like terms: Add 16 to both sides of the equation to isolate the term with x. 8x - 16 + 16 = -40 + 16 8x = -24Add 16 to isolate x: Divide both sides by 8 to solve for x. 8x / 8 = -24 / 8 x = -3Divide by 8 for x: Substitute x = -3 into the second equation to solve for y. The second equation is y = 3x - 4. Substitute -3 for x. y = 3(-3) - 4Substitute x into second equation: Multiply and subtract to find the value of y. y = -9 - 4 y = -13

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Solve the system by substitution.

{:[-4x+4y=-40],[y=3x-4]:}

Solve the system by substitution. $\newline$ $\begin{aligned} -4 x+4 y & =-40 \\ y & =3 x-4 \end{aligned}$

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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} -4 x+4 y & =-40 \\ y & =3 x-4 \end{aligned}

Substitute $y$ with $3x - 4$ : Substitute $y$ with $3x - 4$ in the first equation. $\newline$ The first equation is $-4x + 4y = -40$ and the second equation gives us $y = 3x - 4$ . We will substitute $y$ in the first equation with the expression from the second equation. $\newline$ $-4x + 4(3x - 4) = -40$
Distribute and simplify: Distribute $4$ into the parentheses and simplify. $\newline$ $-4x + 12x - 16 = -40$ $\newline$ Combine like terms. $\newline$ $8x - 16 = -40$
Combine like terms: Add $16$ to both sides of the equation to isolate the term with $x$ . $\newline$ $8x - 16 + 16 = -40 + 16$ $\newline$ $8x = -24$
Add $16$ to isolate $x$ : Divide both sides by $8$ to solve for $x$ . $\newline$ $\frac{8x}{8} = \frac{-24}{8}$ $\newline$ $x = -3$
Divide by $8$ for $x$ : Substitute $x = -3$ into the second equation to solve for $y$ . The second equation is $y = 3x - 4$ . Substitute $-3$ for $x$ . $y = 3(-3) - 4$
Substitute $x$ into second equation: Multiply and subtract to find the value of $y$ . $\newline$ $y = -9 - 4$ $\newline$ $y = -13$