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2x-3y=48

3x+5y=15

2x-3y=48,3x+5y=15

2x-3y=48

2x=3y+48

x=\frac{1}{2}\left(3y+48\right)

x=\frac{3}{2}y+24

3\left(\frac{3}{2}y+24\right)+5y=15

\frac{9}{2}y+72+5y=15

\frac{19}{2}y+72=15

\frac{19}{2}y=-57

y=-6

x=\frac{3}{2}\left(-6\right)+24

x=-9+24

x=15

x=15,y=-6

2x-3y=48

3x+5y=15

2x-3y=48,3x+5y=15

\left(\begin{matrix}2&-3\\3&5\end{matrix}\right)\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}48\\15\end{matrix}\right)

inverse(\left(\begin{matrix}2&-3\\3&5\end{matrix}\right))\left(\begin{matrix}2&-3\\3&5\end{matrix}\right)\left(\begin{matrix}x\\y\end{matrix}\right)=inverse(\left(\begin{matrix}2&-3\\3&5\end{matrix}\right))\left(\begin{matrix}48\\15\end{matrix}\right)

\left(\begin{matrix}1&0\\0&1\end{matrix}\right)\left(\begin{matrix}x\\y\end{matrix}\right)=inverse(\left(\begin{matrix}2&-3\\3&5\end{matrix}\right))\left(\begin{matrix}48\\15\end{matrix}\right)

\left(\begin{matrix}x\\y\end{matrix}\right)=inverse(\left(\begin{matrix}2&-3\\3&5\end{matrix}\right))\left(\begin{matrix}48\\15\end{matrix}\right)

\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}\frac{5}{2\times 5-\left(-3\times 3\right)}&-\frac{-3}{2\times 5-\left(-3\times 3\right)}\\-\frac{3}{2\times 5-\left(-3\times 3\right)}&\frac{2}{2\times 5-\left(-3\times 3\right)}\end{matrix}\right)\left(\begin{matrix}48\\15\end{matrix}\right)

\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}\frac{5}{19}&\frac{3}{19}\\-\frac{3}{19}&\frac{2}{19}\end{matrix}\right)\left(\begin{matrix}48\\15\end{matrix}\right)

\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}\frac{5}{19}\times 48+\frac{3}{19}\times 15\\-\frac{3}{19}\times 48+\frac{2}{19}\times 15\end{matrix}\right)

\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}15\\-6\end{matrix}\right)

x=15,y=-6

2x-3y=48

3x+5y=15

2x-3y=48,3x+5y=15

3\times 2x+3\left(-3\right)y=3\times 48,2\times 3x+2\times 5y=2\times 15

6x-9y=144,6x+10y=30

6x-6x-9y-10y=144-30

-9y-10y=144-30

-19y=144-30

-19y=114

y=-6

3x+5\left(-6\right)=15

3x-30=15

3x=45

x=15

x=15,y=-6