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

Question 1

Which of the following best describes the solution to a system of two linear equations in two variables?

Accepted Answer

The intersection of the two lines on a graph, represented as an ordered pair $$(x, y).$$

Question 2

Given the system $$\begin{cases} 2x - y = -5 \ x + y = 2 \end{cases}$$, what is the solution?

Accepted Answer

$$(4, -2)$$

Question 3

If two lines in a system of linear equations are parallel, what does this imply about the number of solutions?

Accepted Answer

There is no solution.

Question 4

Which step is NOT part of solving a linear system by substitution?

Accepted Answer

Multiply both equations by a constant to eliminate a variable.

Question 5

Solve the system $$\begin{cases} 5x + y = 9 \ -x + 3y = 11 \end{cases}$$ using substitution.

Accepted Answer

$$(1, 4)$$

Question 6

What is the determinant of the matrix $$\left[ \begin{array}{cc} -2 & 3 \ 5 & 1 \end{array} ight]$$?

Accepted Answer

$$-17$$

Question 7

Which of the following systems has infinitely many solutions?

Accepted Answer

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

Question 8

What is the solution to the rational equation $$\frac{x-3}{4} = \frac{5}{14} - \frac{x+5}{7}$$?

Accepted Answer

$$x = -1$$

Question 9

Which interval notation represents all real numbers greater than or equal to $$a$$?

Accepted Answer

$$[a, \infty)$$

Question 10

Solve and graph the inequality $$2 - 3x \leq 5.$$

Accepted Answer

$$x \geq -1$$

Question 11

Given the relation $$\{ (0,2), (3,5), (4,7) \}$$, what is the domain?

Accepted Answer

$$\{0, 3, 4\}$$

Question 12

Which of the following equations does NOT define $$y as a $$function of $$x$$?

Accepted Answer

$$x^2$$ + $$y^2 = 0$

Question 13

If $$f(x) = x^2$ - 2x + 7$$, what is $$f(-5)$$?

Accepted Answer

$$42$$

Question 14

What is the solution to the compound inequality $$1 \leq 2x + 3 \u003c 11$$?

Accepted Answer

$$-1 \leq x \u003c 4$$

Question 15

Which of the following is true about the vertical line test?

Accepted Answer

If a vertical line intersects a graph more than once, it is not a function.

Question 16

What is the determinant of the matrix $$\left[ \begin{array}{cc} -3 & 2 \ 4 & -1 \end{array} ight]$$?

Accepted Answer

$$-5$$

Question 17

Which of the following is the correct solution set for $$1 \leq \frac{x+2}{3} \u003c 5$$?

Accepted Answer

$$1 \leq x \u003c 13$$

Question 18

If a system of three linear equations in three variables has a solution, what does this represent geometrically?

Accepted Answer

The intersection point of three planes in space.

Question 19

What is the solution to the absolute value inequality $$|x-2| \u003c 5$$?

Accepted Answer

$$-3 \u003c x \u003c 7$$

Question 20

Which of the following is NOT a function?

Accepted Answer

$$y^2 = 1$

Systems of Linear Equations, Inequalities, and Functions: Precalculus Study Notes

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