Chapter 11 - Systems of Equations and Inequalities - 11.2 Systems of Linear Equations: Matrices - 11.2 Assess Your Understanding - Page 731: 40

Consistent Solution set: $\{(1,2)\}$

Work Step by Step

We are given the system of equations: $\begin{cases} x+2y=5\\ x+y=3 \end{cases}$ Write the augmented matrix: $\begin{bmatrix}1&2&|&5\\1&1&|&3\end{bmatrix}$ Perform row operations to bring the matrix to the reduced row echelon form: $R_2=-r_1+r_2$ $\begin{bmatrix}1&2&|&5\\0&-1&|&-2\end{bmatrix}$ $R_2=-r_2$ $\begin{bmatrix}1&2&|&5\\0&1&|&2\end{bmatrix}$ $R_1=-2r_2+r_1$ $\begin{bmatrix}1&0&|&1\\0&1&|&2\end{bmatrix}$ Write the corresponding system of equations: $\begin{cases} x=1\\ y=2 \end{cases}$ The system is consistent. Its set solution is: $\{(1,2)\}$

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