Identifying Solutions
Solution to a System of Equations
What is Point of Intersection?
The unique solution to a system of graphs is...
What is where two lines meet or intersect?
Solve by substitution.
y= 12-3x AND y=2x-3
(3,3)
Solve the following system by elimination
x+3y=-7 and -x+2y=-8
(2,-3)
Brianna’s family spent $134 on 2 adult tickets and 3 youth tickets at an amusement park.
Max’s family spent $146 on 3 adult tickets and 2 youth tickets.
What is the price of a youth ticket?
2x+3y=134 and 3x+2y=146;
$22 for a youth ticket.
Is the following ordered pair a solution to the given equations? (7,8)
7x+3y=24
3x+5y=14
What is "no"?
Find the solution for the following equations.
y=x-1
y=2x+2
What is (-3, -4)?
Solve the following equations by substitution.
3x-2y=-3 AND y=7-4x
(1,3)
Solve the Following system by elimination.
x+3y=-4 and 2x-4y=32
(8,-4)
Account A started with $200 and Account B started with $300.
Mr. Malone deposits $15 in Account A and $10 in Account B each month.
In how many months will the accounts have the same balance? What will that balance be?
In 20 months the balance would be $500 in each account.
Is the following ordered pair a solution to the equations? (2,1)
15x+18y=48
25x-9y=41
What is "yes"?
What is the solution to the following equations?
y= -5/3x+3
y= 1/3x-3
What is (3,-2)?
Solve the equations using substitution
4y-2x=-2 AND x=-3y-4
(-1,-1)
Solve the systems of equation using elimination. -10x+y=0 and 5x+3y=-7
(-0.2,-2)
Kate bought 3 used CDs and 1 used DVD at the bookstore. Her friend Joel bought 2 used CDs and 2 used DVDs at the same store. If Kate spent $20 and Joel spent $22, determine the cost of a used CD and a used DVD.
A used CD costs $4.50 A used DVD costs $6.50
Is the ordered pair a solution to the system? (1,3)
2x - 3y = -7
-5x + 3y = 4
What is "yes"?
y=2x-4
y=2x+1
What is "No Solution" or "Parallel"?
Find the solution of the equations by substitution. 3y+6x=9 AND y=-2x-3
no solution
x+16.5=-0.75y and y=0.5x
(-12,-6)
Bhavik bought 3 liters of milk and 5 loaves of bread for a total of $11.
A month later, he bought 4 liters of milk and 4 loaves of bread at the same prices, for a total of $10.
What is the cost of a liter of milk and one loaf of bread?
loaf of bread = $1.75
liter of milk = $0.75
Does the following have a solution? Why or why not? 8x-10y=14
-20x+25y=-35
No, it has infinitely many solutions or same line.
If one equation is y=2x-8 and the solution is (3, -2). Write another equation that could be in the system.
What is....?
-13=2y-3x AND y=-2/3x
(3,-2)
Solve the system of equations using elimination. 2x+y+z=17
0.5z=5 x-y=5
x=4, y=-1. and z=10
If you got this question correct give yourself 1000 points.
The denarius was a unit of currency in ancient Rome. Suppose it costs the Roman government 10 denarii per day to support 4 legionaries and 4 archers.
It only costs 5 denarii per day to support 2legionaries and 2 archers.
Find the unique solution.
There is no unique solution.
The solutions are INFINITE!