Question 1

Given the system of equations:

$\begin{cases} 5x + 3y + 4 = 1 \ -2x - 6y = 3 \end{cases}$

What is the solution to this system?

Accepted Answer

There is no solution because the lines are parallel.

Question 2

What does it mean for a system of equations to be inconsistent?

Accepted Answer

It has no solution because the lines are parallel.

Question 3

If you multiply the first equation in a system by a constant to align coefficients, what is the next logical step in solving by elimination?

Accepted Answer

Add or subtract the equations to eliminate one variable.

Question 4

Given the equation $3y = -x + 4$, what is the slope and y-intercept when written in slope-intercept form?

Accepted Answer

Slope: $-\frac{1}{3}$, y-intercept: $\frac{4}{3}$

Question 5

Rewrite $-6y = 2x + 3$ in slope-intercept form and identify the slope.

Accepted Answer

Slope: $-\frac{1}{3}$

Question 6

If two lines have the same slope but different y-intercepts, what can you conclude about their graphs?

Accepted Answer

They are parallel and never intersect.

Question 7

A system of equations is solved and results in $0 = 11$. What does this indicate about the system?

Accepted Answer

The system is inconsistent and has no solution.

Question 8

Which of the following is the correct slope-intercept form of the equation $3y = -x + 4$?

Accepted Answer

$y = -\frac{1}{3}x + \frac{4}{3}$

Question 9

If you are given the system $2x + 3y = 4$ and $-4x - 6y = 8$, what is the nature of the solution?

Accepted Answer

Infinitely many solutions; the equations represent the same line.

Question 10

Which of the following steps is NOT part of the elimination method for solving systems of equations?

Accepted Answer

Graphing both equations.

Question 11

A real-world scenario: Two companies offer cell phone plans. Company A charges $\$30$ per month plus $\$0.10$ per minute. Company B charges $\$20$ per month plus $\$0.15$ per minute. For what number of minutes will the monthly cost be the same?

Accepted Answer

$200$ minutes

Question 12

Given the equation $y = -\frac{1}{3}x + \frac{3}{6}$, what is the y-intercept?

Accepted Answer

$\frac{1}{2}$

Question 13

If a system of equations has no solution, which of the following must be true?

Accepted Answer

The lines are parallel and have different y-intercepts.

Question 14

Which of the following best describes the solution to a dependent system of equations?

Accepted Answer

Infinitely many solutions.

Question 15

If you are given $y = \frac{1}{3}x + \frac{4}{3}$ and $y = -\frac{1}{3}x + \frac{3}{6}$, what is the solution to the system?

Accepted Answer

$x = 0.75$, $y = 1.25$

Question 16

Which of the following is a necessary condition for two lines to be parallel?

Accepted Answer

They have the same slope but different y-intercepts.

Solving Systems of Linear Equations: Special Cases/Inconsistent 3.1

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