Concepts/Methods
The solution to a system of equations is also known as the ______ __ __________.
Point of intersection
Mr. Sinnott is buying vinyl and CD's. He buys from two different stores. At the RecordStop, he buys 3 vinyl and 2 CD's for 115 dollars. At Newbury Comics, he buys 3 vinyl and 5 CD's for 180 dollars.
3x+2y=115
3x+5y=180
Is (0,0) a solution to the system of inequalities?
y<3x+1
y<-2x+2
Yes
y=3x+2
(3,11)
This method of solving a system starts by scaling our equation(s) to terminate a single variable.
Elimination
LeBron is buying fruits for a party. He buys apples and oranges. The cost of 3 apples and 2 oranges is $12. The cost of 5 apples and 3 oranges is 19$. How much does each fruit cost?
3x+2y=12
5x+3y=19
Is (3,0) a solution to the system of equations:
x+2y=3
2y=3x-9
Yes
5x-y=25
2x+y=17
(6,5)
A method of solving a system that isolates a variable and then plugs in the expression of said variable into another equation.
Substitution
The Buffalo Sabres sold 300 tickets yesterday. Adult tickets (a) cost 10 dollars each and child tickets (c) cost 6 dollars each. If the total revenue of ticket sales from yesterday was 2400, how many adult tickets and children tickets were sold?
a+c=300
10a+6c=2400
Is (-1,5) a solution to the system of inequalities?
x>y-6
3y>2x+4
No
y=-3x+16
y=-2x+11
(5,1)
A unique case of the substitution method that is most effective when we have two equations in slope intercept form.
Equals for equals
Jean Paul Gaultier's farm stand sold a total of 165 pounds of apples and peaches. She sold apples for $1.75 per pound and peaches for $2.50 per pound. If she made $337.50, how many pounds of peaches did she sell?
x+y=165
1.75x+2.50y=337.50
Is (4,-4) a solution to the system of equations?
2y=4x+8
2x=-4y+16
No
7x=5-2y
3y=16-2x
(-1,6)
FINAL JEOPARDY: Describe the solution set for a system of inequalities.
The overlapped shaded region, "waffle" region, double-shaded region.
Where both (or all) inequalities hold true statements.