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

Study Guide - Practice Questions