Linear Equations
Find the solution to the system,
y = -x
y = 2/5x - 7
(5, -5)
Is (2, 6) a solution to this system of inequalities?
y ≥ 6x + 10
y < x + 9
NO
A rental car costs $30 per day plus $0.20 per mile driven. Write the equation to find the total cost, y, for x miles driven in a single day.
What is y = 0.2x+30
Using the vertices (0,0) (1,1) and (2,5) what is the max and min for the equation
T = 2x + 3y
Max = 19
Min = 0
What is the augmented matrices of the following,
x + 3y = 7
-x -5y = 2
1 3 7
-1 -5 2
Find the solution,
y = -2/3x + 2
y = 1/2x - 5
(6, -2)
Is (5, -5) a solution to this system of inequalities?
2x + 18y ≤ 20
7x + y > 8
Yes
An attorney charges a fixed fee of $250 for an initial meeting and $150 per hour for all hours worked after that.
a) What is the value of the y intercept and slope?
b) What would the slope intercept equations look like?
a) 250 and 150x
b) y=150x+250
what is the value of the x and y for the min value,
P = 8x +4y
y ≥ 1/5 x +4
x ≥ 5
y ≤ -1/5 x +8
(5 , 5)
What is the augmented matrices of the following,
x + 2y +z = 5
x + 3z = 7
3x -2y +z = 3
1 2 1 5
1 3 0 7
3 -2 1 3
Using substitution, what would be the easiest first step to solve for,
3x + 2y = 10
-3x + y = 14
BOUNS solve this using Substitution
Solve for y in the second equations.
BOUNS (-2, 8)
What are the vertices of
y ≤ -x +6
x ≥ 0
y ≥ 0
(0,6)
(0,0)
(6,0)
Several times a week, Chuck goes to the gym to run and swim. When running, he burns 35 calories per minute, and when he swims he burns 30 calories per minute. He found a way to burn 730 calories after exercising for a total of 23 minutes. How long does he spend at each activity? use X and Y as variables.
x+y=23
35x+30y=730
Label the Min value and the x and y values.
y ≤ -2x +9
y ≤ 6x +1
y ≥ 2x +1
R = -10x +3y
Min -5 at (2,5)
What is the augmented matrices and the RREF of the following,
2x +2y -z = -3
x + y +z = 6
3x -2y -z = 8
2 2 -1 -3
1 1 1 6
3 -2 -1 8
1 0 0 3
0 1 0 -2
0 0 1 5
Using elimination what would be the first step to solve,
-x +3y = 5
-x -3y = 7
And which variable are you eliminating?
Add the equations to get rid of the y values.
What is the vertices for,
y ≥ -x +10
x ≤ 9
y ≤ 1/2 x +7
y≤ 10
(2,8)
(6,10)
(9,10)
(9,1)
You are at school, 12 miles away from home. You start walking home with your friends at a speed of 3 miles per hour towards your home.
a. Write an equation that represents your distance from home (y) after (x) hours.
b. How many hours does it take to get home?
a. y = -3x + 12
b. 4 hours
What is the max and min values and their x and y values of
y ≥ 0
x ≥ 0
y ≤ -x + 4
C = x - 12y
Max = 4 at (4,0)
Min = -48 at (0,4)
What is the RREF and the solution to the system of,
x - y + 2z = -1
-3x + 3y +5z = 3
2x - 2y = -2
1 -1 0 -1
0 0 1 0
0 0 0 0
Infinite solutions
Using elimination, what would be the easiest first step to solve,
5x + 3y = 8
2x + y = 3
*BOUNS solve using elimination*
Multiplying the bottom equations by -3 to eliminate the y values.
Bonus (1,1)
Find the verticies,
0≤ 2x +3y +15
-20 ≤ 2y + 3x
7x +5y ≤ -25
3x + 5y ≤ -5
(-10,5)
(-5,2)
(-6,-1)
(0,-5)
x+y=18
8x+6y=130
Solution (11,7)
Find the vertices and then find the max value using C= -4x - 5y
0≤ 2x +3y +15
-20 ≤ 2y + 3x
7x +5y ≤ -25
3x + 5y ≤ -5
max = 29
Write out the Augmented Matrix, the RREF, and the Solution to,
3x = -12 -3y
-2y + 2z = 4x -14
x = -3y -2z + 11
3 3 0 -12
-4 -2 2 -14
1 3 2 11
1 0 -1 0
0 1 1 0
0 0 0 1
No solution