Steps to System of Equations
When solving for systems using graphing, we are looking for the _____ of the system.
Intersection. Coordinate point.
What is the Slope Intercept Formula? And tell me what each letter represents. (45)
What is y=mx+b
m is the slope
b in the y intercept
What is the solution to
2x + 9y=0
3x + 5y=17
(9, - 2)
Tell me the slope and y intercept of y=3/4x+8. (30)
3/4
8
x + y = 20
3x + 11y = 100
15,5
When using Substitution, what is the first step?
2x + y =7
2x - 2y = -8
Solve for y in the first equation and the plug into second equation.
What is the formula to find the slope when give two points? (x,y)(x,y) (50)
what is (y2-y1)/(x2-X1)
Delta y over Delta x
What is the solution to
5x + 2y = 48
3x + 2y = 32
(8, 0)
What is the slope and intercept of each line?
2x + y = 8
y - x = 2
First Line S=-2 Y=8
Second Line S=1 Y=2
What is
2x+4y=5
x+2y=8
No solutions. The system is inconsistent.
What is the first step using Elimination?
2x + y=4
5x - y=6
Add the equations together to eliminate y
What is the point slope formula and what does each letter represent? (1 min)
What is y-y1=m(x-x1)
y1 is the y of the coordinate point while x1 is the x of the point. Just flip the signs.
m is still the slope
When two line meet they from a intersection called the solution. In what case would that intercept not be a solution to the inequalities?
When one or both lines are dotted.
What does feasible region mean when graphing inequalities? Draw an example
The shade region that is used as solutions.
Write out the Matrix and then give me the solution
x + 3y = 3
-x + y = -3
[1 3 3]
[-1 1 -3]
(3, 0)
What would we do to solve the system using elimination first?
5x+2y=10
-3x+7y=5
Multiply the top by 3 and the bottom 5.
Find the MAX and MIN value of the vertices using the equation C=5x+2y
Vertices are (-1,4) (3,6) (5,-4)
Max is 27 (3,6)
Min is 3 (-1,4)
-3w +4n = 12
6w-8n =16
No solution
Graphing the following system and tell me what it should look like on a graph.
A. y>2x+1 Dotted/Solid Shade Above/Below
B. x-2y<4 Dotted/Solid Shade Above/Below
Draw all on board
A. Dotted Above
B. Dotted Above
Board
What are the values of X, Y, Z?
2x+2y-z=-3
x+y+z=6
3x-2y-z=8
x= -11
y=1
z=8
Match the steps to the correct System:
x+3y+13 & 3x-2y=-5
5x+3y=8 & 2x+y=3
(Add the equations. Multiply the top by -3. Multiply the bottom by -3.)
x+3y+13 & 3x-2y=-5 Multiply the top by -3
5x+3y=8 & 2x+y=3 Multiply the bottom by -3.
Find the vertex and MAX - MIN value of the vertices using the equation C=8x+11y
All of these are equal to equations
y<_-2x+4
y<_x+7
x+3y>_-3
(-6,1)(3,2)(-1,6)
Max = 58
Min= -37
Explain the difference between
Inconsistent graph,
Consistent-Independent graph, &
Consistent-Dependent graph
Inconsistent is Parallel lines
Con-Independent means it has one solution
Con-Dependent means it has infinite solutions
Chuck goes to the gym to run and swim. When running he burns 35 calories per min, when swimming he burns 30 calories per min. He found a way to burn 730 calories after exercising for 23 min.
Find the system of equations to match this word problem.
x+y=23
35x+30y=730
Does the order triple (-4,2,3) work as a solution for
x+2y+z=5
x+3z=7
3x-2y+z=3
If not what is the solution?
No. 1,1,2