Q: Which of the following systems is inconsistent?

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

Question 1

Which of the following ordered pairs is a solution to the system of equations $$\begin{cases} 2x + y = 10 \ x - y = 2 \end{cases}$$?

Accepted Answer

$$(4, 2)$$

Question 2

What does it mean if the graphs of two linear equations are parallel lines?

Accepted Answer

The system has no solution.

Question 3

Given the system $$\begin{cases} x + y = 3 \ 2x + 2y = 6 \end{cases}$$, what is the nature of its solutions?

Accepted Answer

Infinitely many solutions

Question 4

If the solution to a system of equations is $$(10, 20)$$, what does this mean in the context of the toll bridge problem where $$y = 2x$$ and $$y = x + 10$$?

Accepted Answer

Using the bridge 10 times costs $20 with or without the discount pass.

Question 5

Which of the following systems is inconsistent?

Accepted Answer

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

Question 6

A system of equations is given by $$\begin{cases} 3x - y = 7 \ 6x - 2y = 14 \end{cases}. $$What is true about the solutions?

Accepted Answer

There are infinitely many solutions.

Question 7

Which step is NOT part of solving a system of equations by graphing?

Accepted Answer

Multiply both equations by the same number.

Question 8

If a system of equations has exactly one solution, what does this mean about the graphs of the equations?

Accepted Answer

The lines intersect at one point.

Question 9

Given the system $$\begin{cases} y = 2x + 1 \ y = -x + 4 \end{cases}$$, what is the solution?

Accepted Answer

$$(1, 3)$$

Question 10

Which of the following best describes dependent equations?

Accepted Answer

They represent the same line and have infinitely many solutions.

Question 11

A chemist is mixing two solutions. The cost of solution A is $$y = 5x$$ and the cost of solution B is $$y = 3x + 10. At $$what value of $$x do $$the costs become equal?

Accepted Answer

$$x = 5$$

Question 12

If the lines represented by two equations coincide, what can be said about their solutions?

Accepted Answer

There are infinitely many solutions.

Question 13

Which of the following ordered pairs is NOT a solution to $$x + y = 3$$?

Accepted Answer

$$(2, 2)$$

Question 14

A system of equations is given by $$\begin{cases} y = 4x - 1 \ y = 4x + 3 \end{cases}. $$What is the solution?

Accepted Answer

No solution

Question 15

Which of the following best describes a consistent system?

Accepted Answer

A system with at least one solution

Systems of Linear Equations and Inequalities: Graphical Solutions and Applications

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