Q: Which of the following is the augmented matrix for the system: $$\begin{align*} -4x + 2y &= 20 \\ x + y &= -10 \end{align*}$$

$$\begin{bmatrix} -4 & 2 & | & 20 \\ 1 & 1 & | & -10 \end{bmatrix}$$

Question 1

Solve the following system of equations using Gaussian elimination:

$$\begin{align*}
-4x + 2y &= 20 \
x + y &= -10
\end{align*}$$

What is the solution set $$(x, y)$$?

Accepted Answer

Question 2

Given the system of equations:

$$\begin{align*}
-4x + 2y &= 20 \
x + y &= -10
\end{align*}

If $$you use Gaussian elimination, what is the first row operation you should perform to eliminate $$x$$ from the first equation?

Accepted Answer

Multiply the second equation by $$4$$ and add to the first equation.

Question 3

After performing Gaussian elimination on the system:

$$\begin{align*}
-4x + 2y &= 20 \
x + y &= -10
\end{align*}$$

What is the value of $$y$$?

Accepted Answer

$$y = -2$$

Question 4

Which of the following best describes the solution to the system:

$$\begin{align*}
-4x + 2y &= 20 \
x + y &= -10
\end{align*}$$

Accepted Answer

A unique solution exists.

Question 5

If you substitute $$y = -2$$ into the second equation $$x + y = -10$$, what is the value of $$x$$?

Accepted Answer

$$x = -8$$

Question 6

Which of the following is the augmented matrix for the system:

$$\begin{align*}
-4x + 2y &= 20 \
x + y &= -10
\end{align*}$$

Accepted Answer

$$\begin{bmatrix} -4 & 2 & | & 20 \ 1 & 1 & | & -10 \end{bmatrix}$$

Question 7

Suppose you are solving a system of equations using Gaussian elimination and you obtain a row of all zeros in the coefficient matrix but a nonzero entry in the augmented column. What does this indicate?

Accepted Answer

The system has no solution.

Question 8

Which of the following is NOT a valid row operation in Gaussian elimination?

Accepted Answer

Multiplying a row by zero.

Question 9

If the solution to a system of equations is $$(x, y) = (-8, -2)$$, which of the following statements is true?

Accepted Answer

Substituting $$x = -8$$ and $$y = -2$$ into both equations will satisfy both equations.

Question 10

Which of the following best describes the process of Gaussian elimination?

Accepted Answer

Transforming a system of equations into row-echelon form using row operations.

Solving Systems of Equations: Gaussian and Gauss-Jordan Elimination

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