Solving by Graphing
Draw an example of a point that satisfies only one of the two equations in a system of equation.
**A point that only lies on one of the lines and not at the intersection point**
You are running a concession stand at a basketball game. You are selling hot dogs and sodas.
Each hot dog costs $1.50 and each soda costs $0.50.
At the end of the night you made a total of $78.50.
You sold a total of 87 hot dogs and sodas combined.
Write a system of equations that represents the above situation.
1.50x+0.50y = 78.50
x+y = 87
What form does the solution to a system of equations take?
A ordered (coordinate) pair
(x, y)
Given the system
y = -5x + 14
x = y + 10
What expression belongs in the blank
y = -5( ) + 14
y + 10
Brenda's school is selling tickets to a spring musical. On the first day of ticket sales the school sold 3 senior citizen tickets and 9 child tickets for a total of $75.
The school took in $67 on the second day by selling 8 senior citizen tickets and 5 child tickets.
Suppose the situation above is represented by the system
3x + 9y = 775
8x + 5y = 67
What does x represent in this situation?
What does y represent in this situation?
x = senior citizen tickets
y = child tickets
Convert the following equations into slope-intercept form.
12x+3y=-21
-2x-2y=4
y = -4x-7
y = -x-2
The second number and 4 times the first number add to be 42.
And the second number is equal to 6 more than 2 times the first number.
Write the situation above as a system of equations.
y + 4x = 42
y = 6 + 2x
Given two equations from a system that are graphed on a coordinate plane, describe what the solution to the system looks like.
The intersection point of two equations that are graphed.
Solve the following system using substitution.
y=6x-11
-2x-3y=-7
(2, 1)
Matt and Ming are selling fruit for a school fundraiser. Customers can buy small boxes of oranges and large boxes of oranges.
Matt sold 3 small boxes of oranges and 14 large boxes of oranges for a total of $203.
Ming sold 11 small boxes of oranges and 11 large boxes of oranges for a total of $220.
Find the solution to the system of equations and what the solution means in context.
(7, 13)
small boxes cost $7
large boxes cost $13
Solve the system of equations by graphing
(You may use Desmos)
y = -5x+14
y = x-10
(4, -6)
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.
Write a system of equations that represents the situation above.
3x + y = 38
3x + 2y = 52
What is one way that you could check if your solution to a system of equations is correct?
Either plug it into both of the equations and get a truth statement.
Or graph the two equations and the solution is the intersection point.
Solve the following system using substitution.
-7x-2y=-13
x=11+2y
(3, -4)
All 231 students in the Math Club went on a field trip.
Some students rode in vans which hold 7 students each and some students rode in buses which hold 25 students each.
How many of each type of vehicle did they use if there were 15 vehicles total?
The above system is represented by the following equations
7x+25y = 231
x+y = 15
Suppose the solution to the system is (8, 7).
What does this solution mean in context?
8 vans
7 buses