VOCABULARY
What are the three methods you can use to solve a system of linear equations?
Graphing, Substitution, and Elimination
Solve the System of Equations by Graphing:
y=-1
y=-(5/2)x+4
(2,-1)
Solve the System of Equations by Substitution:
y=5x-7
-3x-2y=-12
(2,3)
Solve the System of Equations by Elimination:
-4x-2y=-12
4x+8y=-24
(6,-6)
Create the System of Equation Represented Below:
The difference of two numbers is 3. Their sum is 13.
x-y=3
x+y=13
5 and 8
What is a solution to a system of linear equations?
The point or points (x,y) at which both lines that represent a system intersect
aka
any point where both lines intersect on the graph
Solve the System of Equations by Graphing:
y=3x-4
y=-(1/2)x+3
Solve the System of Equations by Substitution:
-4x+y=6
-5x-y=21
(-3,-6)
Solve the System of Equations by Elimination:
x-y=11
2x+y=19
(10,-1)
Create the System of Equation Represented Below:
Find the value of two numbers if their sum is 12 and their difference is 4.
x+y=12
x-y=4
4 and 8
What is mean for a system of equations to have no solution?
In a system of linear equations this means the linear are parallel
Solve the System of Equations by Graphing:
y=-(1/2)x-2
y=-(3/2)x+2
(4,-4)
Solve the System of Equations by Substitution:
-7x-2y=-13
x-2y=11
(3,-4)
Solve the System of Equations by Elimination:
2x+8y=6
-5x-20y=-15
Infinitely Many Solutions
Create the System of Equation Represented Below:
There are 13 animals in the barn. Some are chickens and some are pigs. There are 40 legs in all. How many of each animal are there?
x+y=13
2x+4y=40
6 chickens & 7 pigs
What does it mean for a system of linear equations to have infinitely many solutions?
In a system of linear equations the lines are top of each other
aka
the lines have all coordinate points in common on the graph
Solve the System of Equations by Graphing:
y=(1/3)x-3
y=-x+1
(3,-2)
Solve the System of Equations by Substitution:
-3x+3y=4
-x+y=3
No solution
Solve the System of Equations by Elimination:
4x+8y=20
-4x+2y=-30
(7,-1)
Create the System of Equation Represented Below:
Kristin spent $131 on shirts. Fancy shirts cost $28 and plain shirts cost $15. If she bought a Total of 7 then how many of each kind did she buy?
28x+15y=131
x+y=7
2 fancy shirts & 5 plain shirts
What is the definition of a system of linear equations?
Two or more linear equations involving the same variables.
Solve the System of Equations by Graphing:
y=-2x+2
y=-2x-2
No Solution
Solve the System of Equations by Substitution:
x+3y=1
-3x-3y=-15
(7,-2)
Solve the System of Equations by Elimination:
8x+y=-16
-3x+y=-5
(-1,-8)
Create the System of Equation Represented Below:
The school that Stefan goes to is selling tickets to a choral performance. On the first day of ticket sales the school sold 3 senior citizen tickets and 1 child ticket for a total of $38. The school took in $52 on the second day by selling 3 senior citizen tickets and 2 child tickets. Find the price of a senior citizen ticket and the price of a child ticket.
3x+y=38
3x+2y=52
senior citizen ticket=$8
child ticket=$14