Elimination Method
Substitution Method
Graphing to solve
Application
How many solutions?
100
True or False:
When solving a system of equations by using elimination, you always eliminate the "x" variable no matter what.
False: You eliminate the variable that will cancel out when you add or subtract the two equations. Sometimes you need to create this situation by multiplying one or both equations by a constant to get one variable to eliminate.
100
True or False: Given the system below, substitution can be used to replace the 2x with y - 5 and solve for y.
{(2x,+,14y,=,23),(2x,=,y,-,5):}
True: In the two equations you have a "2x" term which is equal to y - 5 in the second equation. You then substitute y - 5 for 2x in the first equation to solve for x.
100
What method can you rely on to help determine if your answer to a system of equations is correct?
The graphing method!!!!
100
Write a system of equations for this situation:
Monday, Cathy bought 4 pounds of gummy bears and 7 pounds of MMs for $21.50. Tuesday, Cathy bought 1 pound of gummy bears and 3 pounds of MMs for $6.
{(4g,+,7m,=,21.50),(g,+,3m,=,6):}
100
The two equations in the system have different slopes.
One solution
200
To eliminate the x-variable, would you rather use subtraction or addition to solve the system? Explain your reasoning.
Subtraction. It eliminates the "x" variables so that you can solve for "y".
200
What would your first step be to solve this system of equations using substitution?
-5(2y-15)+4y=3
200
What is the solution to this system of equations?
(3,-2)
200
Solve the system in the 100 point question in Applications:
{(4g,+,7m,=,21.50),(g,+,3m,=,6):}
($4.50,$0.50)
200
{(x,-,7y,=,11),(2x,=,14y,+77,):}
no solutions
300
To eliminate the y-variable, what would your first TWO steps be in solving this system?
1. Multiply the top equation through by 3.
2. Add the equations.
300
Solve the system by substitution.
(-3,2)
300
The solution to a system of equations is (-4,2). Which graph represents the system?
Graph C
300
This past Saturday, Kern earned $76 removing snow by shoveling for 7 hours and snow blowing for 4 hours. On Sunday, they earned $50 for ONLY snow blowing snow for 10 hours. Solve for the rates this student charges for shoveling snow and snow blowing snow.
The students charges $8/hour for shoveling and $5/hour for snow blowing.
300
The two equations have the same slope, but hit the x-axis at different points
No solutions
400
Solve this system of equations
(2,1)
400
What does x equal?
x = 7.5
400
When you graph a system of equations and only one line appears in the coordinate plane, then you know there are _________ solutions to this system.
oo
400
Write the system of equations that models this situation:
A movie theatre charges different prices for adult tickets than for child tickets. A family of 10 with 2 adults and 8 children can go to the movies for $84. A family of 5 with 3 adults and 2 children go to the movies for $51.
{(2a,+,8c,=,84),(3a,+,2c,=,51):}
400
One equation graphs a vertical line and the other equation graphs a horizontal line.
One solution
500
Solve
(8, -1)
500
Solve this system of four equations:
x=3, y=-2, z=5, w=4
500
Solve this system by graphing.
p = 20.2, q = 10.4
500
Solve this system:
{(2a,+,8c,=,84),(3a,+,2c,=,51):}
($12, $7.50)
500
Which system below has one solution?
A{(x,+,8,=,2/3y),(3x,=,-24,+,2y):}
B{(x,+,6,=,-31),(y,-,x,=,-10):}
B