Question 1

Solve the following system of equations using Gaussian elimination:

$$\begin{cases}
-4x + 2y = 20 \
x + y = -10
\end{cases}$$

What is the solution set?

Accepted Answer

$$\left( -8, -2 \right)$$

Question 2

Which of the following is the correct first step in applying Gaussian elimination to the system:

$$\begin{cases}
-4x + 2y = 20 \
x + y = -10
\end{cases}$$

?

Accepted Answer

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

Question 3

After performing Gaussian elimination on the system:

$$\begin{cases}
-4x + 2y = 20 \
x + y = -10
\end{cases}$$

What is the resulting equation for $$y$$?

Accepted Answer

$$y = -2$$

Question 4

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

Accepted Answer

$$x = -8$$

Question 5

Which of the following best describes the solution to a system of two linear equations that intersect at a single point?

Accepted Answer

The system has a unique solution.

Question 6

What is the geometric interpretation of the solution to the system:

$$\begin{cases}
-4x + 2y = 20 \
x + y = -10
\end{cases}$$

Accepted Answer

The lines intersect at a single point.

Question 7

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

Accepted Answer

Multiplying an equation by zero.

Question 8

If a system of equations has no solution, what does this imply about the graphs of the equations?

Accepted Answer

The lines are parallel and do not intersect.

Question 9

Suppose you have the system:

$$\begin{cases}
2x + 3y = 7 \
4x + 6y = 14
\end{cases}$$

What type of solution does this system have?

Accepted Answer

Infinitely many solutions

Question 10

Which of the following real-world scenarios can be modeled by a system of linear equations?

Accepted Answer

Determining the intersection point of two cost functions in business.

Solving Systems of Equations Using Gaussian Elimination

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