Module 4 Study Guide

Multiple Choice

Write an equation for the line that passes through:

(-4,-7) and (-6,9)

• $$y=8x+39$$  

• $$y=-8x-39$$  

• $$y=-8x-32$$  

• $$y=8x+32$$  

Multiple Choice

Write an equation of the line that passes through

(0 , 10) and (6 , 34)

• $$y=4x+10$$  

• $$y=6x+34$$  

• $$y=4$$  

• $$y=6x-4$$  

Multiple Choice

what is the first step to solve for slope intercept form on

-x + 4y = 11

• subtract 11 from both sides

• add x to both sides

• subtract x from both sides

• put in th y=

Multiple Choice

which of the following is the best first step to solve for y = mx +b? equation is -2x - 4y = -12

• add 4y to both sides

• subtract 2x from both sides

• add 2x to both sides

• divide by -4

Multiple Choice

Find the slope of the following equation. (Hint: put in slope-intercept form)
3x-6y=12

• 3

• -3

• -1/2

• 1/2

Multiple Choice

Write the equation in slope-intercept form:
-10x + 2y = 14

• y = 10x + 12

• y = 10x + 7

• y = 5x + 14

• y = 5x + 7

Multiple Choice

Put the equation in slope-intercept form:
5x - y = 16

• -y = 5x + 16

• y = 5x + 16

• x = 5y - 16

• y = 5x - 16

Multiple Choice

Write an equation of the line that passes through the given point and has the given slope:

$$\left(4,2\right);\ m=\frac{1}{2}$$  

• $$y=\frac{1}{2}x$$  

• $$y=-\frac{1}{2}x$$  

• $$y=\frac{1}{2}x-1$$  

• $$y=\frac{1}{2}x+1$$  

Multiple Choice

Write an equation of the line that passes through the given point and has the given slope:

$$\left(-1,1\right);\ m=4$$  

• $$y=4x+5$$  

• $$y=4x-1$$  

• $$y=4x-3$$  

• $$y=4x-2$$  

Multiple Choice

What is the equation of this line?

• y = 2x +2

• y = 2x -2

• y = -x + 2

• Cannot be Determined

Multiple Choice

Write the equation of the line.

• y = -2/3x + 4

• y = 2/3x + 4

• y = 3/2x + 4

• y = -3/2x + 4

Multiple Choice

What is the y-intercept of this graph?

• (0,1)

• (0,-2)

• (0,0)

• (0,3)

Multiple Choice

Write the equation for the line.

• y= -1x+3

• y= 4x+3

• y=1/4x+3

• y= -4x+3

Multiple Choice

What is the equation for this graph?

• y= 4/5 x + 4

• y= 5/4 x + 4

• y= 4x -5

• y= 5x + 4

Multiple Choice

What is the equation by looking at this graph?

• y= x + 3

• y= -x + 2

• y= 2x + 2

• y= x + 2

Multiple Choice

What is the equation of this line?

• y= -2/3 x -2

• y= 2/3 x -2

• y= -2/3 x + 2

• y= 2

Multiple Choice

Which could be the graph of the equation y = 1/3x - 2?

Multiple Choice

^{What is the solution to the system?} 

• (1,1)

• -2

• (1, 2)

• (1, -1)

Multiple Choice

What is the solution to this system?
y = 2x + 1
y = 4x - 1

• (1,3)

• (-1,-3)

• (-1,3)

• (3,1)

Multiple Choice

Solve by Graphing: What is the solution to this system?

y = 2/3x - 2

y = -x + 3

• (0,3)

• (0,-3)

• (3,0)

• (-3,0)

Multiple Choice

Solve the system by graphing:
y = 6x - 4
y = -x + 3

• (1, 2)

• (2, 1)

• (4, 5)

• (2, 4)

Multiple Choice

Solve the following system by graphing.  What is the solution?

• Infinite number of solutions

• (3, 3)

• (3, -3)

• (-3, 3)

Multiple Choice

Solve the following system by graphing.  What is the solution?

• (1, 2)

• (-1, 2)

• (2, 1)

• (2, -1)

Multiple Choice

Parallel Lines never intersect because...

• they have the same slopes. 

• they have the same y-intercept.

• they have different slopes.

• they have different y-intercepts. 

Multiple Choice

Does the system have one, none or infinite solutions?
8x + 4y = 12
y = -2x + 3

• (0,3)

• (3,0)

• No solution(parallel lines)

• Infinitely many solutions

Multiple Choice

2x - y = 0

4x - y = 0

• (1,2)

• (0,0)

• No Solutions

• Infinite Solutions

Multiple Choice

What is the solution to this system of equations?

• (1,3)

• (0,0)

• No Solution

• (2,0)

Multiple Choice

What is the solution to this equation?

• one solution

• no solution

• infinite solutions

• none of these

Multiple Choice

Is the points (-4, 4) a solution to the system of equations?

• Yes

• No

Multiple Choice

Is the point (2, -1) a solution to the systems of equations below?

y=5x+3

y=-2x-4

• Yes

• No

Multiple Choice

How can you tell if a point is a solution to a system?

• It makes the first equation true.

• The (x,y) coordinates satisfy both equations

• It makes logical sense

• It makes neither equation negative

Multiple Choice

x = x

• No Solution

• One Solution

• Infinite Solutions

• Beyond Solutions

Multiple Choice

How many solutions does this system of equations have?

• One Solution

• No solution

• Infinitely Many Solutions

• Two Solutions

Multiple Choice

Solve:
y = 2x -11
-3y = -6x -15

• (-1.5,-4)

• (1.5,4)

• No solution (parallel lines)

• Infinitely many solutions

Multiple Choice

Solve the following system:

$$y=5x-3$$  

$$3x-8y=24$$  

• $$\left(0,\ -3\right)$$  

• $$\left(0,\ 3\right)$$  

• $$\left(-3,\ 0\right)$$  

• $$\left(3,\ 0\right)$$  

Fill in the Blank

Solve the system by substitution.
 
5x + 4y= −14
y =  −7x  −  15 

Fill in the Blank

Solve for x and y
y = 2x + 1
y = 4x - 1

Fill in the Blank

y = -6x + 5
-2x + y = 5

Multiple Select

What are the 3 ways to solve a system of equations?

SELECT ALL THAT ARE TRUE

• Graphing

• Substitution

• Elimination

Multiple Choice

4x +  8y = 20

-4x + 2y = -30

Which variable will be eliminated first?

• The  x's

• The  y's

• The  z's

Fill in the Blank

4x+9y=28

-4x-y=-28

Solve the system using ELIMINATION.

Open Ended

Solve the system by elimination. What will you use as a multiplier and on which equation? Show all work.

x + 6y = 17

x - 3y = 8

Multiple Choice

What would be the first step in finding the solution using elimination?

2x + 2y = -2

3x - 2y = 12

• you cannot solve this using elimination

• cross out the 2x and 3x

• Add the like terms. The y terms will zero out.

• change to slope intercept form and graph

Multiple Choice

what is the resulting combined equation to the following system:

5x - 4y = 11

5x + 4y = -14

• 5x = -3

• 10y = -3

• 10x = -3

• 10x = -25

Fill in the Blank

Solve by elimination:

3x+7y=23

-3x-7y=-17

Multiple Choice

Solve the system by elimination.

−4x − 4y = 0

4x + 4y = 0

• (−6, −4)

• Infinite number of solutions

• No Solution

• (6, 4)

• (0,0)

Fill in the Blank

Solve by elimination.

6x - y = 2

-3x - 6y = 12

Fill in the Blank

solve using elimination

Multiple Choice

David is running a concession stand at a soccer game. He sells nachos and sodas. Nachos cost $1.50 each and sodas cost $0.50 each. At the end of the game, David made a total of $78.50 and sold a total of 87 nachos and sodas combined. Which system of equations represents this situation?

• 1.5x+0.5y=78.5 x+y=87

• 1.5x+0.5y=78.5 1.5x+0.5y=87

• x+y=78.5 1.5x+0.5y=87

• x+y=78.5 x+y=87

Multiple Choice

Adult tickets to a play cost $22. Tickets for children cost $15. Tickets for a group of 11 people cost a total of $228. What is the number of adult tickets, a, and children tickets, c, that were sold?

• 2 adult tickets, 9 children tickets

• 4 adult tickets, 7 children tickets

• 7 adult tickets, 4 children tickets

• 9 adult tickets, 2 children tickets

Multiple Choice

A snack bar sells two sizes of snack packs. A large snack pack, x, is $5, and a small snack pack, y, is $3. In one day, the snack bar sold 60 snack packs for a total of $220. Which system of equations below can be used to show the number of $5 snack packs and the number of $3 snack packs that were sold?

• x + y = 60

  5x + 3y = 220

• x + y = 60

  3x + 5y = 220

• 5x + y = 60

  x + 3y = 220

• x + 3y = 60

  5x + y = 220

Multiple Choice

August bought a total of 8 pounds of peanuts and cashews. Peanuts, p, cost $4 per pound and cashews, c, cost $6 per pound. The total amount August spent on the peanuts and cashews was $42. Which choice below shows how many pounds of peanuts and cashews August bought?

• 2 pounds of peanuts, 6 pounds of cashews

• 3 pounds of peanuts, 5 pounds of cashews

• 5 pounds of peanuts, 3 pounds of cashews

• 6 pounds of peanuts, 2 pounds of cashews