Question

Solve the system of linear equations using matrices.
\(3x-2y-4=0\)
\(2y=12-x\)

Answer 1

STEP 1
System of linear equation
\(3x-2y=4\)
\(x+2y=12\)
Augmented matrix is
\(\begin{bmatrix}3 & -2 &|&4\\1 & 2 &|&12 \end{bmatrix}\)
Reduring the matrix to reduced
Row echelon form by
Row operations
\(R_1\rightarrow \frac{1}{3}R\)
\(\begin{bmatrix}1 & \frac{-2}{3} &|&\frac{4}{3}\\1 & 2 &|&12 \end{bmatrix}\)
\(R_2 \rightarrow R_2-R_1\)
\(\begin{bmatrix}1 & \frac{-2}{3} &|&\frac{4}{3}\\0 & \frac{8}{3} &|&\frac{32}{3} \end{bmatrix}\)
\(R_2 \rightarrow \frac{8}{3}R_2\)
\(\begin{bmatrix}1 & \frac{-2}{3} &|&\frac{4}{3}\\0 & 1 &|&4 \end{bmatrix}\)
Step2
\(R_1 \rightarrow R_1+\frac{2}{3}R_2\)
\(\begin{bmatrix}1 & 0 &|&4\\0 & 1 &|&4 \end{bmatrix}\)
\(\Rightarrow x =4\)
\(y=4\)
Thus solution of system is \(x=4 , y=4\)