Vocabulary
What is a limitation on the values in an equation called?
A constraint
In what form is this equation?
Ax + By = C
Standard Form
x + y = 3
4x + 5y = 14
Is (1,2) a solution this this system of equations?
yes
(substitute x=1 and y=2 to verify that it is true!)
On which axis would this point be located?
(0, 6)
The y-axis
4x + 5y = 20
What would the first move be to convert this equation to slope-intercept form?
Subtract (move) the term with 4x
What is a system of equations?
Two or more related equations
In what form is this equation?
y = mx + b
slope-intercept form
Name at least two ways to solve a system of equations.
graphing
substitution
elimination
On which axis is this point located?
(2, 0)
The x-axis
5y = -4x + 20
How would you isolate the y?
Divide each term by 5
Two equations that have the same solution are what type of equations?
Equivalent equations
4 + 5 = 10
Is this a true equation?
Why or why not
No, because the two sides are not equal
Without graphing, what would be an efficient way to solve this system of equations? Be specific!
2x + 3y = 10
-2x + y = 2
Elimination, adding the equations eliminates the x variable
What is another name for (0, 0)?
The origin
2x + 9(3x - 6) = 99
What would you do first to begin solving this equation?
Distribute the 9
What is a quantity that may change in an equation?
a variable
What is the m in
y = mx + b?
the slope
How many solutions would this system of equations have?
x + y = 2
2x + 2y = 4
infinite (these equations are equivalent)
y = 4x + 2
What point does the "2" represent in this equation? Give the ordered pair!
(0, 2)
the y-intercept
3a + 6 = 15
3a = 9
What move can change the first equation to the second?
Subtract 6 from both sides
What is a pair of coordinates that make two equations true?
A solution to a system of equations
What is the b in
y = mx + b?
The y - intercept. Where the line crosses the y axis
Find the solution:
3x + 2y = 20
3x - 2y = 4
(4,4)
2x + 3y = 12
Find the x and y intercept of this equation.
x-int: (6,0)
y-int: (0,4)
5x=24+2x
3x=24
What move was made to change the first equation to the second equation?
Subtract 2x from both sides