Solve the system by substitution. {:[-3x+3y=-12],[y=5x-8]:}

Substitute y with 5x - 8: Substitute y with 5x - 8 in the first equation. -3x + 3y = -12 becomes -3x + 3(5x - 8) = -12.Distribute 3 to terms: Distribute 3 to the terms inside the parentheses. -3x + 3(5x) - 3(8) = -12 -3x + 15x - 24 = -12Combine like terms: Combine like terms. 12x - 24 = -12Add 24 to isolate: Add 24 to both sides of the equation to isolate the term with x. 12x - 24 + 24 = -12 + 24 12x = 12Divide both sides: Divide both sides by 12 to solve for x. 12x / 12 = 12 / 12 x = 1Substitute x = 1: Substitute x = 1 into y = 5x - 8 to solve for y. y = 5(1) - 8 y = 5 - 8 y = -3

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Solve the system by substitution.

{:[-3x+3y=-12],[y=5x-8]:}

Solve the system by substitution. $\newline$ $\begin{aligned} -3 x+3 y & =-12 \\ y & =5 x-8 \end{aligned}$

View step-by-step help

Home

Math Problems

Algebra 2

Solve a system of equations in three variables using substitution

Full solution

Q. Solve the system by substitution.

\newline

\begin{aligned} -3 x+3 y & =-12 \\ y & =5 x-8 \end{aligned}

Substitute $y$ with $5x - 8$ : Substitute $y$ with $5x - 8$ in the first equation. $\newline$ $-3x + 3y = -12$ becomes $-3x + 3(5x - 8) = -12$ .
Distribute $3$ to terms: Distribute $3$ to the terms inside the parentheses. $\newline$ $-3x + 3(5x) - 3(8) = -12$ $\newline$ $-3x + 15x - 24 = -12$
Combine like terms: Combine like terms. $12x - 24 = -12$
Add $24$ to isolate: Add $24$ to both sides of the equation to isolate the term with $x$ . $12x - 24 + 24 = -12 + 24$ $12x = 12$
Divide both sides: Divide both sides by $12$ to solve for $x$ . $\newline$ $\frac{12x}{12} = \frac{12}{12}$ $\newline$ $x = 1$
Substitute $x = 1$ : Substitute $x = 1$ into $y = 5x - 8$ to solve for $y$ .
$y = 5(1) - 8$
$y = 5 - 8$
$y = -3$