Solve the linear system $3x+4y=10$ $2x-y=3$ using the matrix inverse method.

Step-by-step solution

1. Write the coefficient matrix A=\begin{pmatrix}3&4\2&-1\end{\pmatrix} and the constant vector b=\begin{pmatrix}10\3\end{\pmatrix}.
2. Compute the determinant $detA=3(-1)-4(2)=-3-8=-11$.
3. Find the inverse A^{-1}=\frac{1}{-11}\begin{pmatrix}-1&-4\-2&3\end{\pmatrix}.
4. Multiply $A^{-1}$ by $b$: A^{-1}b=\frac{1}{-11}\begin{pmatrix}-1&-4\-2&3\end{\pmatrix}\begin{pmatrix}10\3\end{\pmatrix}=\frac{1}{-11}\begin{pmatrix}-10-12\-20+9\end{\pmatrix}=\frac{1}{-11}\begin{pmatrix}-22\-11\end{\pmatrix}.
5. Simplify to get $x=2,;y=1$.

Concept tested: Solving linear equations using matrix inverse

Published 13 October 2026 · How this solution was prepared and checked