Question

Solve the following system of linear equations.

3x + 2y = 10
2x + 3y = 15/2

Answer 1

By Gaussian reduction:
\[
\begin{align}
3(3x+2y)&=2(10)\\
2(2x+3y)&=2(\frac{15}{2})
\end{align}
\]Which becomes:
\[
\begin{align}
9x+6y&=30\\
4x+6y&=15
\end{align}
\]Subtracting one from the other gives us one nice equation:
\[
5x=15\implies\\
x=3
\]Plugging this value into the above:
\[
3(3)+2y=10\implies\\
2y=1\implies\\
y=\frac{1}{2}
\]As a check:
\[
2(3)+3(\frac{1}{2})=6+\frac{3}{2}=\frac{15}{2}
\]Hence, we are done.