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Solve the system by substitution.

{:[2x+7y=48],[x=6y+5]:}

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Solve the system by substitution. $\newline$ $\begin{aligned} 2 x+7 y & =48 \\ x & =6 y+5 \end{aligned}$ $\newline$ $(\square, \square)$

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Identify independent and dependent variables: word problems

Full solution

Q. Solve the system by substitution.

\newline

\begin{aligned} 2 x+7 y & =48 \\ x & =6 y+5 \end{aligned}

\newline

(\square, \square)

Substitute $x$ in first equation: Substitute the value of $x$ from the second equation into the first equation. $\newline$ We have $x = 6y + 5$ . We will substitute this into the first equation $2x + 7y = 48$ .
Replace $x$ in equation: Replace $x$ in the first equation with the expression from the second equation. $\newline$ $2(6y + 5) + 7y = 48$
Distribute and combine terms: Distribute $2$ to the terms inside the parentheses. $\newline$ $12y + 10 + 7y = 48$
Isolate y term: Combine like terms. $\newline$ $19y + 10 = 48$
Solve for $y$ : Subtract $10$ from both sides of the equation to isolate the term with $y$ . $19y = 38$
Substitute $y$ back for $x$ : Divide both sides by $19$ to solve for $y$ . $\newline$ $y = \frac{38}{19}$ $\newline$ $y = 2$
Calculate x value: Substitute the value of $y$ back into the second equation to solve for $x$ . $\newline$ $x = 6y + 5$ $\newline$ $x = 6(2) + 5$
Calculate $x$ value: Substitute the value of $y$ back into the second equation to solve for $x$ .
$x = 6y + 5$
$x = 6(2) + 5$ Calculate the value of $x$ .
$x = 12 + 5$
$x = 17$

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