Simplify the expression by combining like terms:
2x+7+5x-2
7x+5
Sketch an example of the graph of a system of linear equations with only one solution.
(on board, lines intersect)
Which is a more accurate method, solving systems of linear equations by graphing the lines or by "doing the math"?
Doing the math - you get an exact point
When graphing a linear inequality on the coordinate plane, what symbols tell you to use a dotted line?
< or >
TRUE or FALSE: A Zillion is a real number.
False! A zillion is not an actual quantity... it is just used to refer to a large amount.
Solve the one-step equation:
x/3=7
x=21
Sketch an example of the graph of a system of linear equations with an infinite amount of solutions.
(on board, overlapping lines)
What are the 3 "solution types" that systems of linear equations can have?
One solution, no solutions, infinite solutions
When solving systems of linear inequalities, instead of looking for where lines intersect, we are looking for where shaded areas _______.
Overlap
How many digits are there in Pi?
An infinite amount!
Use the Order of Operations to simplify:
(11-2) div (2+6-5)
3
Sketch an example of the graph of a system of linear equations with no solutions.
(on board, parallel lines)
Name and describe one of the two methods we can use to solve a system of linear equations.
1. Substitution: set equations equal to one another or plug part of one equation in to the other
2. Elimination: use addition/subtraction between each term in the equations to eliminate one variable
Is it possible for two parallel lines in a system of linear inequalities to have a solution? How is this different from parallel lines in a system of linear equations?
Yes; linear equations that are parallel will not overlap (no solutions)
A perfect number is equal to the sum of its factors (other than the number itself). For example, Factors of 28 are 1, 2, 4, 7, 14, and 28. 1+2+4+7+14= 28. What is the smallest perfect number?
HINT: It is between 1 and 10.
6
(1+2+3=6)
Use the vertical line test to determine whether or not the graph represents a function:
It is a function
With slopes of (2/3) and y-intercepts of 2 and -1, write the equations for these two lines. How many solutions are in this system?
y=2/3x+2 and y=2/3x-1; no solutions
Solve the system of linear equations:
y=-4x+7
y=5x-20
(3,5)
Graph the inequality:
y<=-2x+6
0 (zero) has more synonyms (words that have the same meaning) than any other number. Name two other synonyms for zero.
zilch, nada, nil, zip, naught, etc.
Evaluate the function for f(-2):
f(x)=2x-4
-8
Graph the system of linear equations and identify the solution as a coordinate point:
y=2x-3
y=-4x+3
(1,-1)
Solve the system of linear equations:
y=x+6
y=-2x-15
Graph the system of linear inequalities:
y<=x-2
y> -3x+5
Honeybees construct their hives using this geometric shape, which maximizes space and structural stability in a mathematically efficient way.
Hexagons