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$Find the solution of the system of equations. {:[x+3y=13],[-x+2y=12]:} (_________,________)$

Find the solution of the system of equations. $\newline$ $\begin{aligned} x+3 y & =13 \\ -x+2 y & =12 \end{aligned}$ $\newline$ $\newline$ (_,)

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Write an equation word problem

Full solution

Q. Find the solution of the system of equations.

\newline

\begin{aligned} x+3 y & =13 \\ -x+2 y & =12 \end{aligned}

\newline

\newline

(_________,________)

Add Equations Together: Add the two equations together to eliminate $x$ . $(x + 3y) + (-x + 2y) = 13 + 12$ $3y + 2y = 25$ $5y = 25$
Divide to Solve for y: Divide both sides by $5$ to solve for $y$ . $\frac{5y}{5} = \frac{25}{5}$ $y = 5$
Substitute $y$ into First Equation: Substitute $y = 5$ into the first equation to solve for $x$ . $x + 3(5) = 13$ $x + 15 = 13$
Subtract to Solve for x: Subtract $15$ from both sides to solve for $x$ . $\newline$ $x + 15 - 15 = 13 - 15$ $\newline$ $x = -2$

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