3.3E: Exercises - Solving Systems with Gauss-Jordan Elimination

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Write an augmented matrix to represent each system of equations.

1) $\begin{align*} 5x-y &= 4\\ x+6y &= 2 \end{align*}$

2) $\begin{align*} -3x-5y &= 13\\ -x+4y &= 10 \end{align*}$

3) $\begin{align*} 3x+7y &= 1\\ 2x+4y &= 0 \end{align*}$

Write each augmented matrix as a system of equations.

4) $ \left[ \begin{array}{rr|r} -4&3&5 \\ 2&-1&1 \end{array}\right]$

5) $ \left[ \begin{array}{rrr|r} 1&5&2&4 \\ -2&9&0&-4 \\ 2&-1&1&5 \end{array}\right]$

6) $ \left[ \begin{array}{rrr|r} 1&0&0&-2 \\ 0&1&0&3 \\ 0&0&1&7 \end{array}\right]$

Use Gaussian Elimination to solve each system of equations.

7) $\begin{align*} 5x+9y &= 16\\ x+2y &= 4 \end{align*}$

8) $\begin{align*} \dfrac{1}{3}x+\dfrac{1}{9}y &= \dfrac{2}{9}\\ -\dfrac{1}{2}x+\dfrac{4}{5}y &= -\dfrac{1}{3} \end{align*}$

9) $\begin{align*} -0.2x+0.4y &= 0.6\\ x-2y &= -3 \end{align*}$

10) $\begin{align*} 3x+6y &= 11\\ 2x+4y &= 9 \end{align*}$

11) $\begin{align*} x+y+z &= 197\\ -2x+y &= 6\\x+y-z&=37 \end{align*}$

12) $\begin{align*} 2x-y+3z &= 17\\ -5x+4y-2z &= -46\\2y+5z&=-7 \end{align*}$

Write a system of equations to represent each scenario. Then use Gaussian elimination to solve for the desired quantity.

13) A cell phone factory has a cost of production $C(x)=150x+10,000$ and a revenue function $R(x)=200x$. What is the break-even point?

14) The startup cost for a restaurant is $\$120,000$, and each meal costs $\$10$ for the restaurant to make. If each meal is then sold for $\$15$, after how many meals does the restaurant break even?

15) If an investor invests a total of $\$25,000$ into two bonds, one that pays $3\%$ simple interest, and the other that pays $2\dfrac{7}{8}\%$ interest, and the investor earns $\$737.50$ annual interest, how much was invested in each account?

Contributors and Attributions

Jay Abramson (Arizona State University) with contributing authors. Textbook content produced by OpenStax College is licensed under a Creative Commons Attribution License 4.0 license. Download for free at https://openstax.org/details/books/precalculus.