Q: Which of the following systems has no solution?

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

Question 1

Given the linear equation $$2x - 3y = 6$$, what is the slope of the line?

Accepted Answer

Question 2

What is the y-intercept of the line given by the equation $$y = -4x + 7$$?

Accepted Answer

$$7$$

Question 3

A company charges a flat fee of $$\50$ plus $$\$$20$$ per hour for consulting. Which equation models the total cost $$C$$ for $$h$$ hours?

Accepted Answer

$$C = 20h + 50$$

Question 4

Which of the following best describes the graph of the equation $$x = 3$$?

Accepted Answer

A vertical line crossing the x-axis at $$x = 3$$

Question 5

Find the x-intercept of the line $$4x + 2y = 8.$$

Accepted Answer

$$(2, 0)$$

Question 6

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

Accepted Answer

They are parallel and never intersect.

Question 7

Solve the system: $$\begin{cases} x + y = 5 \ x - y = 1 \end{cases}$$

Accepted Answer

$$(3, 2)$$

Question 8

Which of the following systems has no solution?

Accepted Answer

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

Question 9

A line passes through the points $$(1, 2)$$ and $$(3, 6). $$What is its slope?

Accepted Answer

$$2$$

Question 10

Which of the following equations represents a line with a y-intercept of $$-3$$ and a slope of $$\frac{1}{2}$$?

Accepted Answer

$$y = \frac{1}{2}x - 3$$

Question 11

A chemist mixes two solutions: one with 30% salt and one with 10% salt. If she wants 10 liters of a 20% solution, how many liters of the 30% solution should she use?

Accepted Answer

$$5$$

Question 12

Which of the following is the correct graph for the equation $$y = -x + 2$$?

Accepted Answer

A line with slope $$-1$$ crossing the y-axis at $$2$$

Question 13

If a system of two linear equations has infinitely many solutions, what must be true about the two lines?

Accepted Answer

They are the same line.

Question 14

A taxi company charges $$\3$ for the first mile and $$\$$2$$ for each additional mile. Which equation models the total cost $$C$$ for $$m$$ miles ($$m \geq 1$$)?

Accepted Answer

$$C = 3 + 2(m-1)$$

Question 15

Which of the following points lies on the line $$y = 3x - 4$$?

Accepted Answer

$$(2, 2)$$

Question 16

If the equation of a line is $$y = mx + b$$ and $$m = 0$$, what kind of line is it?

Accepted Answer

A horizontal line

Question 17

A medical researcher finds that the number of flu cases $$C in a $$city can be modeled by $$C = 50t + 200$$, where $$t is $$the number of weeks since the start of flu season. What does the number $$200$$ represent?

Accepted Answer

The initial number of flu cases at the start of the season

Question 18

Which of the following is the solution to the system $$\begin{cases} 2x + y = 7 \ x - y = 1 \end{cases}$$?

Accepted Answer

$$(2, 3)$$

Question 19

A line has a slope of $$-\frac{3}{4}$$ and passes through the point $$(0, 5). $$What is its equation?

Accepted Answer

$$y = -\frac{3}{4}x + 5$$

Question 20

Which of the following best describes the solution to a system of two linear equations that are perpendicular?

Accepted Answer

They intersect at exactly one point.

Linear Equations in Two Variables and Systems of Linear Equations

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