Q: Which of the following systems is inconsistent?

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

Q: Which of the following systems has infinitely many solutions?

$$\begin{cases} 2x + 3y = 6 \\ 4x + 6y = 12 \end{cases}$$

Question 1

Which of the following is the correct slope-intercept form of the equation $$2x + y = 4$$?

Accepted Answer

$$y = -2x + 4$$

Question 2

Given the system of equations:

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

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

Accepted Answer

$$(1.0, -1.0)$$

Question 3

Which method would be most efficient for solving the system $$\begin{cases} 3x - 2y = 5 \ 2x + y = 3 \end{cases}$$?

Accepted Answer

Elimination (addition/subtraction) method

Question 4

If you solve $$\begin{cases} 3x - 2y = 5 \ 2x + y = 3 \end{cases} by $$elimination, what is the value of $$x$$?

Accepted Answer

$$x = 2$$

Question 5

A smelter needs to produce 42 tonnes of copper ore containing 4.2% copper by mixing two ores: one with 6.0% copper and one with 2.4% copper. How many tonnes of the 6.0% copper ore are needed? (Round to 1 decimal place)

Accepted Answer

27.6 tonnes

Question 6

Which of the following systems is inconsistent?

Accepted Answer

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

Question 7

What is the determinant of the coefficient matrix for the system $$\begin{cases} 2x + y = 4 \ x - 2y = 1 \end{cases}$$?

Accepted Answer

$$-5$$

Question 8

If the determinant of a system's coefficient matrix is zero, what does this indicate about the system?

Accepted Answer

The system has either no solution or infinitely many solutions.

Question 9

Given the system $$\begin{cases} 4x + 3y = 8 \ 2x - y = 1 \end{cases}$$, solve for $$y$$ using the substitution method.

Accepted Answer

$$y = 1$$

Question 10

Which of the following best describes the graphical solution to the system $$\begin{cases} y = 2x + 3 \ y = -x + 1 \end{cases}$$?

Accepted Answer

The lines intersect at exactly one point.

Question 11

A chemist needs to mix two solutions: one with 10% acid and one with 30% acid to obtain 100 mL of a 25% acid solution. How many mL of the 30% solution should be used?

Accepted Answer

75 mL

Question 12

Which of the following is the correct solution for $$x in $$the system $$\begin{cases} x + 2y = 5 \ 3x - y = 4 \end{cases}$$?

Accepted Answer

$$x = 1.4$$

Question 13

If you graph the equation $$y = -2x + 4$$, what is the $$y-$$intercept?

Accepted Answer

$$4$$

Question 14

Which of the following systems has infinitely many solutions?

Accepted Answer

$$\begin{cases} 2x + 3y = 6 \ 4x + 6y = 12 \end{cases}$$

Question 15

A system of equations is given by $$\begin{cases} 2x + 3y = 7 \ 4x + 6y = 14 \end{cases}. $$What is the relationship between the two equations?

Accepted Answer

They are dependent.

Question 16

Which of the following is the correct solution for $$y in $$the system $$\begin{cases} 2x + y = 4 \ x - 2y = 1 \end{cases}$$?

Accepted Answer

$$y = -1$$

Question 17

A system of equations is solved using determinants:

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

What is the value of the determinant of the coefficient matrix?

Accepted Answer

$$-11$$

Question 18

Which of the following is NOT a valid method for solving a system of two linear equations?

Accepted Answer

Quadratic formula

Question 19

If a system of equations models the intersection of two roads, what does a unique solution represent in real life?

Accepted Answer

The roads intersect at a single point.

Question 20

Which of the following is the correct solution for $$x in $$the system $$\begin{cases} 4x + 3y = 8 \ 2x - y = 1 \end{cases}$$?

Accepted Answer

$$x = 2$$

Systems of Equations and Methods of Solution (Chapter 5 Review)

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