Facts about system
How can we tell that our equations are linear?
They have an exponent of 1.
You attend an Eagles game. At the first food stall, the price of nachos is $4 and a beverage is $2 and you spent $12. At another food stall the price of nachos is $2 and a beverage is $1 and you spent $8. Write a system to represent both food stalls.
Final Answer
n=nacho
b=beverage
4n+2b=12
2n+b=8
Solve the system of linear equations by graphing:
x + y = 7
y = x + 3
Final Answer
(2,5)
Solve this System of Linear Equations using Substitution...TAKE YOUR TIME!!
y=5x+2
y=2x+8
(x,y)=(2,12)
Solve this System of Linear Equations using Elimination...TAKE YOUR TIME!!
x + 2y = 5
x + y = 2
Final answer
(x,y)=(-1,3)
What are the three methods we learned to solve a system of linear equations?
Graphing, Substitution, Elimination
At a basketball game, all tickets are the same price and all souvenirs are the same price. Bobby bought 2 tickets to this basketball game and 1 souvenir for a total of $17.25. Emily bought 5 tickets to the same game and 2 souvenirs for a total of $42.00. Set up a system of linear equations for this situation.
2t + s = 17.25
5t + 2s = 42
Solve the system of linear equations by graphing:
y = 2x + 5
y = 0.5x - 1
Final Answer
(x,y)=(-4,-3)
Solve this System of Linear Equations using Substitution...TAKE YOUR TIME!!
x + y = 4
2x + 4y = 6
(x,y)=(5,-1)
Solve this System of Linear Equations using Elimination...TAKE YOUR TIME!!
4x + 2y = 10
2x + 2y = 12
Final answer
(x,y)=(-1,7)
How can you verify that your solution is correct?
If you plug back your answer into a given system then it should satisfy the system.
The cost of three notebooks and four pencils is $8.50.
The cost of five notebooks and eight pencils is $14.50.
Set up a system of equations and determine the cost of one notebook and the cost of one pencil.
x=Note Book; y=Pencils
3x+4y=8.50
5x+8y=14.50
x=Note book=$2.50
y=pencil=$0.25
Solve the following system of linear equations graphically?
y=(1/2)x - 2
y=4x+5
Final answer
(x,y)=(-2,-3)
Solve this System of Linear Equations using Substitution...TAKE YOUR TIME!!
x - 3y = -14
3x + y = 8
(x,y)=(1,5)
Solve this System of Linear Equations using Elimination...TAKE YOUR TIME!!
6x + 8y = 14
6x + 13y = 19
Final Answer
(x,y)=(1,1)
How many solutions are in this System of Linear Equations?
y+19x=8
y-19x=8
One solution
Slope of first equation is -19.
Slope of 2nd equation is +19.
A farmhouse shelters 10 animals. Some are pigs and some are ducks. Altogether there are 36 legs.
Set up a system of equations and tell how many pigs and ducks are there?
Final answer
8 pigs and 2 ducks.
Solve the following system of linear equations graphically?
y = x - 7
y + x = 3
Final Answer
(5,-2)
Solve the system of linear equations by substitution:
y - x = 0
2x - 5y = 9
Final answer
(-3,-3)
Solve this System of Linear Equations using Elimination...TAKE YOUR TIME!!
3x + 2y = 9
2x + 6y = 6
Final Answer
(x,y)=(3, 0)
When solving a system of linear equations algebraically, how do you know when the system has no solution?
When solving a system of linear equations algebraically, how do you know when the system has infinitely many solutions?
No solution:
When we end up with a false statement or if slope of both equations is same but different y-intercept.
Infinitely many solutions
When we end up with a true statement or if slope of both equations is same and y-intercept is also same.
Mr. Green is buying halloween candy to prepare for next year. He has $75 to spend (he wants to spend all of it), and he is buying king size twix bars for $3 and a regular pack of starburst for $2. He buys a total of 25 items of candy.
Write the system of equations that represent this word problem.
Final Answer
75=3t+2s
25=t+s
Solve the system of linear equations by substitution:
2x = y - 10
x + 7 = y
Final Answer
(-3,4)
Solve this System of Linear Equations using Elimination...TAKE YOUR TIME!!
-x + 5y = 8
3x + 7y = -2
Final Answer
(-3, 1)