August 2023
Simplify using exponents:
a x a x a x a = ?
a4
Solve for x:
15 - 2x = 9
x = 3
What is the constant of proportionality in the following equation?
y = 1.75x
1.75
A set of two (or more) equations to solve together.
What method would you use to solve the following system of equations:
2x + 4y = 16
-2x + 3y = 5
Elimination
43 = ?
64
Solve for x:
8x + 4 = 4x + 8
x = 1
4 pounds of grapes cost $5. What is the cost per pound?
Grapes cost $1.25 per pound
How do we write the solution to a system of equations?
As an ordered pair Ex: (x, y)
What does the graph of a system of equations look like when it has one solution?
Two lines that cross each other at one point.
Simplify using exponents:
23 x 27 = ?
210
Solve for x:
3x - 4x + 2 + 5x + 4 = 46
x = 10
Write the formula for the equation of a line written in slope intercept form:
y = mx + b
What 3 methods did we learn in order to solve systems of equations?
Graphing
Substitution
Elimination
What does the graph of a system of equations look like when it has no solution?
2 Parallel lines
49/45 = ?
44
Solve for x:
12 - 9x = -3(x + 10)
x = 7
What is the slope and y-intercept of the following equation?
y = -1.5x + 8
slope = -1.5
y-intercept = 8
Solve the following system of equations: (25 bonus points if you can name the best method to use)
y = x + 5
y = 4
(-1, 4)
Substitution
What does the graph of a system of equations look like when it has infinitely many solutions?
It looks like just one line since the lines are exactly the same line.
If I have $305.000, how much money do I have?
1 dollar
Solve for x:
8x - 22 = 3(3x + 11) - x
No solution
Find the slope of a line that passes through the points (1, -2) and (4, 7)
slope = 3
Solve the following system of equations:
y = -3x - 5
y = 3x + 7
(-2, 1)
Write the following as an equation:
Six more than four times a number is twenty-five
4x + 6 = 25
OR
6 + 4x = 25
Write the following in standard form:
1.6 X 103
1,600
Solve for x:
2x - 5(x + 1) - 6 = 3(x + 4) + 1
x = -4
Given the slope and the y-intercept, write the equation of the line in slope intercept form:
A slope of 2/3 and a y-intercept of -3
y = 2/3x -3
Is the following set of ordered pairs a function? Please state why or why not?
(1 , 2)
(0 , 1 )
(-1 , 0)
(1 , 1)
NO! Each input (x) has to have only one output (y).
Write the following as an equation:
Fifteen less than one-eighth of a number is 16
1/8(x) - 15 = 16
Write 79,700 in scientific notation.
7.97 X 104
Write an equation and solve:
Fish tank A has 95 gallons of water and is losing 4 gallons per day. Fish tank B has 50 gallons of water and 5 gallons are being added each day. How many days will it take for the tanks to have the same amount of water?
5 days
Write an equation to match the following scenario:
Verizon wireless charges new customers a $70 sign up fee and $25 per month.
y = 25x + 70
Solve the following system of equations. (25 bonus points for stating the method used):
-2x - 3y = -7
y = 6x - 11
(2, 1)
Substitution
Solve the following using Elimination:
10x - 3y = 18
-2x + 3y = 6
(3, 4)