Solve the system by substitution. {:[3y=x],[-3x+6y=6]:} (◻,◻)

Identify Variable Isolation: Identify the first equation where one variable is already isolated. The first equation is 3y = x. This equation can be used to substitute for x in the second equation.Substitute in Second Equation: Substitute 3y for x in the second equation -3x + 6y = 6. Substitute x with 3y in -3x + 6y = 6 to get -3(3y) + 6y = 6.Simplify and Solve for y: Simplify and solve for y. -9y + 6y = 6 Combine like terms to get -3y = 6. Divide both sides by -3 to solve for y. y = -2Substitute Back to Find x: Substitute y = -2 back into the first equation 3y = x to find x. 3(-2) = x x = -6Write Solution as Ordered Pair: Write the solution as an ordered pair (x, y). The solution is (-6, -2).

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Solve the system by substitution.

{:[3y=x],[-3x+6y=6]:}

(◻,◻)

Solve the system by substitution. $\newline$ $\begin{array}{r} 3 y=x \\ -3 x+6 y=6 \end{array}$ $\newline$ $(\square, \square)$

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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{array}{r} 3 y=x \\ -3 x+6 y=6 \end{array}

\newline

(\square, \square)

Identify Variable Isolation: Identify the first equation where one variable is already isolated. $\newline$ The first equation is $3y = x$ . This equation can be used to substitute for $x$ in the second equation.
Substitute in Second Equation: Substitute $3y$ for $x$ in the second equation $-3x + 6y = 6$ . Substitute $x$ with $3y$ in $-3x + 6y = 6$ to get $-3(3y) + 6y = 6$ .
Simplify and Solve for y: Simplify and solve for y. $\newline$ $-9y + 6y = 6$ $\newline$ Combine like terms to get $-3y = 6$ . $\newline$ Divide both sides by $-3$ to solve for y. $\newline$ $y = -2$
Substitute Back to Find $x$ : Substitute $y = -2$ back into the first equation $3y = x$ to find $x$ . $3(-2) = x$ $x = -6$
Write Solution as Ordered Pair: Write the solution as an ordered pair $(x, y)$ . The solution is $(-6, -2)$ .