How many Solutions?
Solve by Graphing
Solve by Substitution
Solve by Elimination
WiLd CaRd QuEsTiOnS
100
Is there 1 solution, No solution, or Infinite solutions for the system of linear equations below?
One Solution (-4,-6)
100
What is the solution?
(-1,1)
100
Solve the systems of equations using substitution:
y = -2x - 9
3x -6y = 9
(-3, -3)
100
Solve the systems of equations using Elimination:
14x + 2y = 26
-14x - 6y = -50
(1, 6)
100
Why do we need to check the solution for both equations when we verify?
The solution is the point of intersection. So we need to verify with both equations to make sure the point is on both lines.
200
Is there 1 solution, No solution, or Infinite solutions for the system of linear equations below?
y = 3x - 5
y = 3x + 7
No Solutions
200
What is the solution?
No Solutions
200
Solve the systems of equations using substitution:
-5x - 5y = 10
y = -4x -17
(-5, 3)
200
Solve the systems of equations using Elimination:
-x - 8y = -22
3x + 4y = -14
(-10, 4)
200
Verify the solution: (2,6)
y = 2x + 2
y + 2x = 12
Not Valid
300
Is there 1 solution, No solution, or Infinite solutions for the system of linear equations below?
y = (-5/3)x + 3
y = (1/3)x - 3
1 solution
300
Solve Using Graphing:
y = 5/3x + 2
y = -3
300
Solve the systems of equations using substitution:
2x - 4y =16
-4x + 5 = y
(2, -3)
300
Solve the systems of equations using elimination:
x - 3y = 10
2x + y = 6
(4, -2)
300
Create the equations to model the following situation. DO NOT SOLVE!
A 500-space parking lot is filled with motorcycles and cars, with only one vehicle in each space. How many motorcycles and cars are there if the total number of tires on the parked vehicles is 1650?
Use:
m - motorcycles
c - cars
m + c = 500
2m + 4c = 1650
400
Is there 1 solution, No solution, or Infinite solutions for the system of linear equations below?
y = 3x + 9
4x - 2y = 18
One Solution
400
How many solutions are there?
Infinitely Many Solutions
400
Solve the systems of equations using substitution:
x + y = 6
3x - 2y = -2
(2,4)
400
Solve the systems of equations using elimination:
x + y = 132
2y - 3 = x
(87, 45)
400
Verify the solution: (3, 2)
4x - y = 10
-2x + y = -4
Valid
500
Is there 1 solution, No solution, or Infinite solutions for the system of linear equations below?
18x - 4y = 12
-9x + 2y = -6
Infinitely Many Solutions
500
Solve the systems of linear equations by graphing:
500
Solve the systems of equations using substitution:
x - 3y = -9
2x + 7y = 8
(-3,2)
500
Solve the systems of equations using Elimination:
-5x + 2y = -12
4x - 3y = 11
(2, -1)
500
Create the equations to model the following situation. Then, solve for points!
An amusement park charges one admission price for adults and another for children under 12. The Joe family has two adults and three children under 12. The cost for their admission is $80. The Mack family has three adults and one child under 12. Their admission cost is $99. What is the price for an adult ticket and a child's ticket?
Use:
a - adult
c - children
2a + 3c = 80
3a + c = 99
adults = $31
children = $6