One Solution
No Solution
Infinite Solutions
Graphing
Word Problems
100

What does it mean to have one solution?

One solution means if you solve the equation and get a variable equal to a number.

100

What does it mean to have no solution?

No solution means there is no value, not even 0, which would satisfy the equation.

100

What does it mean to have infinite solutions? 

Infinite solutions means to have both sides of the equation equal. 

100

Graph: y = 1/2x -2 and y = -1/2 x -4

Draw the graph to show the solution to the system of equations.

(-2, -3)

100

At Crazy Skates, a roller skating rink, skaters purchase a ticket to enter and pay an additional fee to rent skates if needed. The cost per ticket is $2 less than twice the cost of renting skates. A group of friends purchased 9 tickets and 6 skate rentals for a total $102. Which systems for equations can be used to find x, the cost of renting skates, and y, the cost per ticket?

y = 2x -2

6x + 9y = 102

200

Does 2x + 1 = 9 equal one Solution?

Yes, 2x + 1 = 9 equals one Solution 

x = 4

200

Does 3x + 5 = 3x - 5 equal no solution?

Yes 3x + 5 = 3x - 5 equals no solution

0 = -10

200

Does x + 3 = 2x equal infinite solutions?

No, x + 3 = 2x equals one solution.

x = 3

200

Graph: y = 2x -5 and -x + 2y = 2

Draw the graph to show the solution to the system of equations. 

(4, 3)

200

There are 30 dumbbells in Mindy's barre studio. Each dumbbell weights either 3 pounds or 5 pounds, and the combined weight of all 30 dumbbells is 126 pounds. Which system of equations can be used to find the number of 3-lb weight, x, and the number of 5-lb weight, y, that are in the studio?

x + y = 30

3x + 5y = 126

300

Does 5x + 10 = 6x -20 equal one solution?

Yes 5x + 10 = 6x -20 equals one solution

x = 30

300

Does 6x + 9 = 6x + 19 equal no solution?

Yes 6x + 9 = 6x + 19 equals no solution

0 = 10

300

Does 2x + 3 =2(x +4) equal infinite solutions?

No, 2x + 3 =2(x +4) equals no solutions.

0=5

300

Lin graphed one equation from a series of equations as shown. If Lin's system has no solution, which of the following could be the 2nd equation.

A. x - 3y = -9                                B. -2x+ 6y = 12

C. 2x + 6y = -18                           D. x -2y = -9


B. -2x + 6y = 12

300

At a company dinner party, guests could choose between beef or chicken tacos. A total of 180 guests ate at the party, and the number of people who chose beef tacos was 68 more than one third the number of people who chose chicken tacos. Let x represent the number of people who chose chicken and y represent the number of people who chose beef. How many guests chose beef and how many chose chicken?

x = 84

y = 96

400

Does 2x + 3 = 8 equal one solution?

Yes, 2x + 3 = 8 equals one solution

x = 5/2

400

Does 4(2x−8)=8(x−4) equal no solution?

No, 4(2x−8)=8(x−4) equals infinite solutions 

0 = 0

400

Does (8x -2y = -10) + (4x -y = -5) equal infinite solutions? Solve by using elimination. 

Yes, (8x -2y = -10) + (4x -y = -5) equals infinite solutions

0=0

400

The line represents the first of two equations in a system of equations. If the second line contains the points (-6, 3) and (9, -7), find the solution of system.

A. (6, 5)                                        B. (-6, -6)

C. Infinite Solutions                        D. No Solution

C. Infinite Solutions

400

Angles P and Q are supplementary angles with a sum of 180∘ . If the measure of Angle P is 15 more than two times the measure of Angle Q, how many degrees is the measure of Angle P?

P = 125∘ 

500

Does 4x + 2x + 6 = 6x + 2 + 4 equal one solution? 

No, 4x + 2x + 6 = 6x + 2 + 4 equals infinite solutions.

0=0

500

Does 13x−5(x−4)=8x+5 equal no solution?

Yes, 13x−5(x−4)=8x+5 equals no solution

20 = 5 

500

Does 7(8x+5)−35= 4(14x) equal to infinite solutions.

Yes 7(8x+5)−35= 4(14x) equals infinite solutions 

0 = 0

500

On the white board record which graph each student created to solve their system of equations. Then, write the solution to the system.

Dakota: 

Solution: (4,-5) Graph: C

Angel: 

Solution: (0,4) Graph: B

Jordan:

Solution: (-6,3) Graph: A

500

The school nurse took a total of 68 student's temperatures last month. The number of students who had a fever was 7 less than one-forth of the students who did not have a fever. How many students did not have a fever? Let x represent the number of students who had a fever and y represent the number of students who did not have a fever.

y = 60 

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