Linear Equations
Substitution
Elimination
Linear Inequalities
Vocabulary
100
What does the Range represent (all of the x or y values)
What is all of the y-values
100
y = 2
3x + 2y = 10
(2, 2)
100
x + 3y = 5
2x − 3y = −8
(−1, 2)
100
What does a dotted line mean when graphing linear inequalities?
> or <
100
Consists of two or more linear equations in the same variables.
System of linear equations (linear system)
200
What are the 3 major forms of linear equations?
Point-slope form, standard form, and slope intercept
200
x = −3y + 2
−x + 2y = 3
(−1, 1)
200
−5y + 8x = −18
5y + 2x = 58
(4, 10)
200
How is graphing systems of inequalities different than graphing systems of equations? (2 things)
Sometimes they use dotted lines and you have to shade for inequalities.
200
The method of solving equations where you add or subtract equations to end up with one variable.
Elimination
300
Zaman has sar500 in her account. If she earns sr50 per day working for her dad what is an equation to represent how much money(y) she will have in x days.
What is y = 50x + 500
300
x − 2y = −10
3x = y
(2, 6)
300
3y − 5x = −26
−2y − 5x = −16
(4, −2)
300
How do you know where to shade when solving systems of inequalities?
The solution is where the shaded regions overlap.
300
How can you tell if a linear system has infinitely many solutions?
The equations are the same, the graphed lines lie on top of one another.
400
What is the first point you would plot if you were given y - 2 = 4(x - 5)?
What is (5, 2)?
400
2x – 3y = –2
y = −4x + 24
(5, 4)
400
3x − 4y = 8
18x − 5y = 10
(0, -2)
400
What type of line should be used when graphing an inequality with an "or equal to" symbol?
A Solid Line
400
When will a system of linear inequalities have no solution?
The inequalities are parallel meaning they have the same slope but different y-intercepts and shaded away from each other. (Not in opposite directions)
500
What is the y- intercept of the table?
The y- intercept is b=25.
500
5x − 13 = y
−5x + y = 24
no solution
500
4x−9y = 2
12x−5y = −38
(-4, -2)
500
Based on the graph below, where would we find a solution to the system of inequalities?
Any point that lands in the shaded region
500
How can you tell that a point is a solution to a system of inequalities?
The point must land in BOTH shaded areas (The point of intersection)