Graphing Systems of Equations
State whether the systems of equations is:consistent or inconsistent; independent or dependent; one or no or infinite
y=-3/2x + 5
y=-2/3x +5
Consistent, Independent, and One Solution
Use Substitution!!! to solve each system of equations
y = 5x + 1
4x + y = 10
(1,6)
Use ELIMINATION to solve each system of equations.
-4x + 5y = 17
4x + 6y = -6
(-3 , 1 )
When graphing linear inequalities, what does < and > mean?
Use a dashed line.
Write the system of equations in slope intercept form
state whether they are (consistent, inconsistent, independent, dependent, one, no, infinite solutions)
2x+5=2x+5
y=2x+5 & y=2x+5
Consistent, Dependent, Infinite many
State whether the systems of equations is:consistent or inconsistent; independent or dependent; one or no or infinite solutions
x+y=4
3x+3y=12
Consistent, Dependent, and Infinite
Use Substitution!!! to solve each system of equations
y = -3x + 4
-6x -2y = -8
Infinitely solutions
Use elimination to solve each systems of equations
2x + 5y = 11
4x + 3y = 1
( -2 , 3 )
Solve each system of inequalities by graphing.
y < x + 10
y > 6x + 2
How many solutions are there?
Is (0,3) a solution?
Graph
Infinite
No
State whether the system is consistent independent, inconsistent, consistent dependent and has one, no, or infinite solutions. How can you determine without solving?
4x + 3y = 6
12y + 16x = 24
Consistent dependent, infinite solutions.
The slopes and y-intercepts are the same (they are the same equation/line).
State whether the systems of equations is:consistent or inconsistent; independent or dependent; one or no or infinite solutions
2x + y = 4
y = -2x -2
Inconsistent, No solutions
Use Substitution!!! to solve each system of equations
5x - y = 5
-x + 3y = 13
(2,5)
Use elimination to solve each systems of equations
12x - 3y = -3
6x + y = 1
( 0 , 1 )
Solve each system of inequalities by graphing.
x + y < -1
x + y > 3
How many soutions are there?
Is (0,0) a solution?
Graph
No solutions
No
The difference of the two numbers is 2. Find the ordered pair.
( -2 , -4 )
Graph the system and state the solution.
y = 1/2 x + 2
y = 1/4 x + 4
(8, 6)
Use Substitution!!! to solve each system of equations
y = 3.2x + 1.9
2.3x + 2y = 17.72
(1.6 , 7.02)
The art teacher purchased 5 lbs of firing clay and 24 lbs of polymer clay for $64.05. The next time she ordered, she tried to reduce her total cost and purchased 25 lbs of firing clay and 8 lbs of polymer clay for $51.45. Create the system of equations, solve and interpret the solution in the context of the problem.
5x + 24y = 64.05
25x + 8y = 51.45
(1.29, 2.40) The cost of the firing clay is $1.29, and the cost of the polymer clay is $2.40.
Write a System of Inequalities for the solution shown.
Show Picture
y > x
y < 1
Two times a number plus three times another number equals 13.
The sum of the two numbers is 7.
Find the numbers.
( 8 , -1 )
Graph the system and state the solution.
4x + 5y = 15
8x + 5y = 45
(5, 1)
Use Substitution!!! to solve each system of equations
y = -10x -6.8
-50x - 10.5y = 60.4
(-.2 , -4.8)
Sam and Ben each bought snacks for their friends. Sam bought four bags of popcorn and two bags of chips. Ben bought seven bags of popcorn and two bags of chips. Sam paid $18.50 and Ben paid $26.75.
Write the system of equations, solve, and explain the solution in the context of the problem.
4x + 2y = 18.50
7x + 2y = 26.75
(2.75, 3.75) A bag of popcorn costs $2.75 and a bag of chips costs $3.75.
Write a System of Inequalities for the solution shown.
Show picture
x < 2
y < 3
y > -1/3 x
Solve the system.
3x - 2y + 5z = -17
2x + 4y - 3z = 29
5x - 6y - 7z = 7
(2, 4, -3)