System of Equations
What 2 variables do we usually use in a system of equations?
x and y
y = 2x +6
y = -4/3 x -2
What are the y-intercepts of these equations?
6 and -2
What is the first step to solving a system by substitution?
Isolate one of the variables in the equations.
Write the system. x = dogs and y = cats. You have 15 cats and dogs and it costs $5 for dog tags and $3 for cat tags. You spent $63 on tags altogether.
x + y = 15
5x + 3y = 63
What popular social media app, launched in 2016, allows users to share short videos with music and effects?
Tik Tok
How many equations are in a system of equations?
Two or more
When graphing the line
y = -2x +4
How would you graph starting from the y-intercept, which is 4?
Down 2 to the right 1.
Isolate the x variable from this equation.
2y + x = 12
x = -2y +12
Write the system. You and a friend go to Tacos Galore for lunch. You order 3 soft tacos and 3 burritos and your total bill is $11.25. Your friend's bill is $10.00 for 4 soft tacos and 2 burritos.
3x + 3y = 11.25
4x + 2y = 10
Which ancient civilization built the famous city of Machu Picchu in the Andes Mountains?
The Incas
What is the solution to a system of equations?
Where the lines intersect
What needs to be done to graph this system?
y - 2x = 4
4x + y = -6
Change into slope- intercept form.
The second step is substituting the isolated variable. Substitute for x in the second equation and simplify.
x = -2y + 12
y = 3x -1
y = 3 (-2y +12) - 1
y = -6y + 36 - 1
y = -6y + 35
7y = 35 Final Answer: y = 5
Write the system: You are working two part-time jobs. Working at the local library pays $15/hr and working as a personal trainer pays $20/hr. Last week you made $800 and worked 45 total hours.
x + y = 45
15x + 20y = 800
In grammar, what is the term for a word that describes a noun or pronoun, often indicating quality or state of being (e.g., "happy," "blue")?
An Adjective
When do a system of equations have infinitely many solutions?
When the equations are the same line.
Change this system into slope-intercept form.
y - 2x = 4
4x + y = -6
y = 2x + 4
y = -4x - 6
Now that we know y = 5, solve the remaining variable x.
x = -2y + 12
y = 3x -1
x = 2
Write the system. 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.
x + y = 87
1.5x + .5y = 78.5
What is the name for the element with the chemical symbol 'Au' on the periodic table, often associated with wealth and jewelry?
Gold
When does a system of equations have no solution?
When both equations are parallel to each other.
Solve the system by graphing.
y = 3/2x + 2
y = -2x - 5
(-2, -1)
Solve this system using substitution.
x - 2y = 8
x = 5 - y
(6, -1)
Write the system: You open a business to make and sell custom bracelets. You purchase office equipment and a laptop to market and sell your product which costs $1150. The cost to manufacture one bracelet is $2.40 and you plan to sell them for $11.
y = 2.40x + 1150
y = 11x
What is the strongest muscle in the human body?
The jaw muscle