Solve the system by substitution. {:[3x-8y=9],[x=3y+6]:} (◻,◻)

Identify Equation for Substitution: Identify the equation that can be used for substitution. We are given the system of equations: 3x - 8y = 9 x = 3y + 6 The second equation, x = 3y + 6, is already solved for x, which makes it easy to substitute into the first equation.Substitute x into First Equation: Substitute x = 3y + 6 into the first equation. Substitute the expression for x from the second equation into the first equation: 3(3y + 6) - 8y = 9Distribute and Combine Terms: Distribute and combine like terms. 3(3y) + 3(6) - 8y = 9 9y + 18 - 8y = 9 Combine like terms: (9y - 8y) + 18 = 9 y + 18 = 9Solve for y: Solve for y. Subtract 18 from both sides of the equation to isolate y: y + 18 - 18 = 9 - 18 y = -9Substitute y into Second Equation: Substitute y = -9 into the second equation to find x. Substitute y = -9 into x = 3y + 6: x = 3(-9) + 6Calculate x Value: Calculate the value of x. x = -27 + 6 x = -21Write Solution as Ordered Pair: Write the solution as an ordered pair (x, y). The solution to the system of equations is (-21, -9).

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Solve the system by substitution.

{:[3x-8y=9],[x=3y+6]:}

(◻,◻)

Solve the system by substitution. $\newline$ $\begin{aligned} 3 x-8 y & =9 \\ x & =3 y+6 \end{aligned}$ $\newline$ $(\square, \square)$

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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{aligned} 3 x-8 y & =9 \\ x & =3 y+6 \end{aligned}

\newline

(\square, \square)

Identify Equation for Substitution: Identify the equation that can be used for substitution. $\newline$ We are given the system of equations: $\newline$ $3x - 8y = 9$ $\newline$ $x = 3y + 6$ $\newline$ The second equation, $x = 3y + 6$ , is already solved for $x$ , which makes it easy to substitute into the first equation.
Substitute $x$ into First Equation: Substitute $x = 3y + 6$ into the first equation. $\newline$ Substitute the expression for $x$ from the second equation into the first equation: $\newline$ $3(3y + 6) - 8y = 9$
Distribute and Combine Terms: Distribute and combine like terms. $\newline$ $3(3y) + 3(6) - 8y = 9$ $\newline$ $9y + 18 - 8y = 9$ $\newline$ Combine like terms: $\newline$ $(9y - 8y) + 18 = 9$ $\newline$ $y + 18 = 9$
Solve for y: Solve for y. $\newline$ Subtract $18$ from both sides of the equation to isolate $y$ : $\newline$ $y + 18 - 18 = 9 - 18$ $\newline$ $y = -9$
Substitute $y$ into Second Equation: Substitute $y = -9$ into the second equation to find $x$ . $\newline$ Substitute $y = -9$ into $x = 3y + 6$ : $\newline$ $x = 3(-9) + 6$
Calculate x Value: Calculate the value of x. $\newline$ $x = -27 + 6$ $\newline$ $x = -21$
Write Solution as Ordered Pair: Write the solution as an ordered pair $(x, y)$ . The solution to the system of equations is $(-21, -9)$ .