What does it mean to have one solution?
One solution means if you solve the equation and get a variable equal to a number.
What does it mean to have no solution?
No solution means there is no value, not even 0, which would satisfy the equation.
What does it mean to have infinite solutions?
Infinite solutions means to have both sides of the equation equal.
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)
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
Does 2x + 1 = 9 equal one Solution?
Yes, 2x + 1 = 9 equals one Solution
x = 4
Does 3x + 5 = 3x - 5 equal no solution?
Yes 3x + 5 = 3x - 5 equals no solution
0 = -10
Does x + 3 = 2x equal infinite solutions?
No, x + 3 = 2x equals one solution.
x = 3
Graph: y = 2x -5 and -x + 2y = 2
Draw the graph to show the solution to the system of equations.
(4, 3)
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
Does 5x + 10 = 6x -20 equal one solution?
Yes 5x + 10 = 6x -20 equals one solution
x = 30
Does 6x + 9 = 6x + 19 equal no solution?
Yes 6x + 9 = 6x + 19 equals no solution
0 = 10
Does 2x + 3 =2(x +4) equal infinite solutions?
No, 2x + 3 =2(x +4) equals no solutions.
0=5
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
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
Does 2x + 3 = 8 equal one solution?
Yes, 2x + 3 = 8 equals one solution
x = 5/2
Does 4(2x−8)=8(x−4) equal no solution?
No, 4(2x−8)=8(x−4) equals infinite solutions
0 = 0
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
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
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∘
Does 4x + 2x + 6 = 6x + 2 + 4 equal one solution?
No, 4x + 2x + 6 = 6x + 2 + 4 equals infinite solutions.
0=0
Does 13x−5(x−4)=8x+5 equal no solution?
Yes, 13x−5(x−4)=8x+5 equals no solution
20 = 5
Does 7(8x+5)−35= 4(14x) equal to infinite solutions.
Yes 7(8x+5)−35= 4(14x) equals infinite solutions
0 = 0
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
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