Conceptual
A solution to a system of linear equations is written as what?
BE SPECIFIC
What is a coordinate point?
What is an ordered pair?
You and your friend are at the football game. You buy two popcorns, p, for $6. Your friend buys 2 popcorns, p, and a Fanta, f, for $9.50.
What is the solution(s) to our system, of linear equations? Write your answer in the form of ( p , f ).
USE UNITS OF MEASURE
What is ($3, $3.50)?
Is the ordered pair ( -1 , 1 ) a solution to the linear system below?
Remember an ordered pair is in the form (x, y)
-x + 2y = 3
y = x + 3
What is no? It works for the top one, but not the bottom.
Solve this system of equations using any method:
Remember a solution to a system of linear equations is in the form (x,y). Simplify your answer if possible.
y = -2x + 4
y = 2x - 6
What is (2.5, -1)?
How many solutions are there to the following system of linear equations?
y = -x - 2
y = -x - 5
What is one?
A system of linear equations which has no solutions contains two equations which might be described as what when graphed?
What are parallel lines?
You have 9 packages of toilet paper. Some packages have 3 rolls, but other packages have only 1 roll. In all, there are 20 rolls.
Write a system of linear equations to model this scenario. You do not need to solve. Use x and y for variables.
What is x + y = 9 and 3x + y = 20.
What is x + y = 9 and x + 3y = 20.
Is the ordered pair (3,2) a solution to this system of linear equations?
2x + 3y = 12
x − y = 1
What is yes?
Solve this system of equations using any method:
Simplify your answer if possible.
3y = 3x + 9
-½x + y = 3
What is (0 , 3)?
How many solutions are there to the following system of linear equations?
y - x = 5
x + y = 5
What is one?
How many solutions are there to the equation:
y = 2x + 3
What is infinite solutions?
You have some $1 bills and $5 bills. In all, you have 9 bills worth $25.
Write a system of linear equations to model this scenario. You do not need to solve. Use x and y for variables.
What is x + y = 9 and x + 5y = 25
What is x + y = 9 and 5x + y = 25
Is the ordered pair (-1, 2) a solution to this system of linear equations?
2x − y = 4
4x − 2y = 10
What is no. The lines are parallel so there are no solutions.
Solve this system of equations using any method:
Simplify your answer if possible.
2x + y = 12
3y = 8x + 1
What is (2.5, 7)?
How many solutions are there to the following system of linear equations?
y = x - 6
3y = 3x - 6
What is none?
You can solve a system of equations by adding or subtracting the equations in such a way that one variable drops out. This is called the ____________ method
What is elimination?
You have some $2 bills and $5 bills. In all, you have 7 bills worth $29.
Write a system of linear equations to model this scenario. You do not need to solve. Use x and y for variables.
What is 5x + 2y = 29 and x + y = 7?
What is 2x + 5y = 29 and x + y = 7?
How many solutions are there to the following system of linear equations?
2x + y - x = 3
6x + 2y - 4x = 6
What is infinitely many?
The admission fee at a small fair is $1.50 for children and $4.00 for adults. On a certain day, 2200 people enter the fair and $5050 is collected. How many children and how many adults attended?
Write a system of equations to match the situation then solve. Write your answer in the form of (c , a)
c + a = 2200
$1.50c + $4.00a = $5050
Solved:
(1500, 700)