# Chapter 2 - Matrices - Review Exercises - Page 98: 20

$$x=\frac {18}{11},\quad y= -{\frac {19}{11}}.$$

#### Work Step by Step

We have the system $$\left[\begin{array}{rrr}{2} & {-1} \\{3}& {4} \end{array}\right]\left[\begin{array}{rrr}{x}\\ {y} \end{array}\right]=\left[\begin{array}{rrr}{5} \\ {-2} \end{array}\right].$$ The coefficients matrix $A=\left[\begin{array}{rrr}{2} & {-1} \\{3}& {4} \end{array}\right]$ has the inverse $$A^{-1}=\left[ \begin {array}{cc} \frac{4}{11}&\frac{1}{11}\\ -\frac{3}{11}&\frac{2}{11} \end {array} \right] .$$ The system has the solution $$\left[\begin{array}{rrr}{x}\\ {y} \end{array}\right]=\left[ \begin {array}{cc} \frac{4}{11}&\frac{1}{11}\\ -\frac{3}{11}&\frac{2}{11} \end {array} \right]\left[\begin{array}{rrr}{5} \\ {-2} \end{array}\right]=\left[ \begin {array}{c} {\frac {18}{11}}\\ -{ \frac {19}{11}}\end {array} \right] .$$ That is $$x=\frac {18}{11},\quad y= -{ \frac {19}{11}}.$$

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.