elimination
Should we add or subtract the two equations to eliminate a variable?
x + 3 y = 5
2x - 3y = -8
Add
What variable should you substitute?
y = x + 1
2x + y =10
y
What is the y-intercept and the slope of BOTH equations?
y = 2x + 2
y = x - 1
y = 2x + 2
y-int: 2 , slope: 2/1
y=x-1
y-int: -1 , slope: 1/1
what are the 3 methods of solving systems of equations
elimination
graphing
substitution
when graphing linear inequalities what does < and > mean
It is less than or greater then and not equal to and use a dotted line
What would you multiply to be able to eliminate a variable using the elimination method?
4x - 9y = 2
12x - 5y = -38
Multiply the first equation by 3.
(other correct answer will be accepted)
Solve using substitution.
y = 2
3x + 2y = 10
(2,2)
Find the two zero coordinates of BOTH equations you would find to plot these lines.
-2x+ y = 6
-x+ y = 3
-2x+ y = 6
( 0 , 6 ) , ( -3 , 0 )
-x+ y = 3
( 0 , 3 ) , ( -3 , 0)
How can you tell if a linear system has infinitely many solutions from graphing?
the equations are the same and the lines lie on top of each other
what does ≤ and ≥ mean when graphing linear inequalities
It is less than or greater then and equal to and use a solid line
Solve using elimination.
4x - 3y = 16
5x + 3y = 20
(4,0)
Solve using substitution.
y = 5x - 1
2y = 3x + 12
(2,9)
Find the two important items you would find to plot each line.
3x - 2y = 6
y = -x + 6
3x - 2y = 6
( 0 , -3 ) , ( 2 , 0 )
y = -x + 6
y-intercept: + 6 , slope: -1/1
what does it mean when the lines are parallel or they have the same slope and different y-intercepts or when you solve the equations and get a false statement with no variables remaining.
no solution
Label on each inequality if you will have a solid or dashed line and if you will shade above and below.
y ≤ x − 2
y > −3x + 5
y ≤ x − 2
solid line, shade below
y > −3x + 5
dashed line, shade above