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$Find the solution of the system of equations. {:[3x-6y=-45],[x-6y=-47]:} $\newline$(_________,________)"$

Find the solution of the system of equations. $\newline$ $\begin{array}{r} 3 x-6 y=-45 \\ x-6 y=-47 \end{array}$ $\newline$ (_,)

Full solution

Q. Find the solution of the system of equations.

\newline

\begin{array}{r} 3 x-6 y=-45 \\ x-6 y=-47 \end{array}

\newline

(_________,________)

Eliminate y by subtraction: Subtract the second equation from the first to eliminate y. $\newline$ $(3x - 6y) - (x - 6y) = (-45) - (-47)$
Simplify subtraction: Simplify the subtraction. $3x - x = -45 + 47$
Calculate difference: Calculate the difference. $2x = 2$
Solve for x: Divide both sides by $2$ to solve for x. $x = \frac{2}{2}$
Substitute $x$ into second equation: Simplify the division. $x = 1$
Add $6y$ to both sides: Substitute $x = 1$ into the second equation to solve for $y$ . $1 - 6y = -47$
Calculate sum: Add $6y$ to both sides. $\newline$ $6y = 1 + 47$
Solve for $y$ : Calculate the sum. $6y = 48$
Simplify division: Divide both sides by $6$ to solve for $y$ . $\newline$ $y = \frac{48}{6}$
Simplify division: Divide both sides by $6$ to solve for $y$ . $\newline$ $y = \frac{48}{6}$ Simplify the division. $\newline$ $y = 8$