Solve by Graphing
Solve by Substitution
Solve by Elimination
Systems in General
Definitions & more...
100
What is the solution?
(-1,1)
100
Solve the systems of equations using substitution:
-3x + 4y = -2
y = -5
(-6, -5)
100
Solve the systems of equations using Elimination:
14x + 2y = 26
-14x - 6y = -50
(1, 6)
100
What strategy would you use?
14x + 2y = 26
-14x - 6y = -50
elimination
100
Graphically, solutions of a system of two equation correspond to this.
What is points of intersection?
200
How many solutions are there?
No Solutions
200
Solve the systems of equations using substitution:
-5x - 5y = 10
y = -4x -17
(-5, 3)
200
Solve the systems of equations using Elimination:
-3x - 5y = 2
3x + 5y = 7
No Solution
200
What strategy would you use?
-5x - 5y = 10
y = -4x -17
substitution
200
The first step in solving in a system of equations by substitution..
What is solve one of the equations for one variable in terms of the other?
300
Solve Using Graphing:
y = 5/3x + 2
y = -3
300
Solve the systems of equations using substitution:
x + y = - 9
5x -8y = 20
(-4, -5)
300
Solve the systems of equations using Elimination:
3x + 4y = -26
2x + 5y = 18
(-2, -5)
300
Is there 1 solution, No solution, or Infinite solutions for the system of linear equations below?
3x - y = 19
-3x + y = 10
No Solutions
300
The 4 methods we learned in this class to solve systems of equations.
What is
1. Substitution
2. Elimination
3. Graphing
4. Gaussian elimination or row echelon form
400
How many solutions are there?
Infinitely Many Solutions
400
Solve the systems of equations using substitution:
2x - y2 = 0
x - y = 4
(8, 4), (2,-2)
400
Solve the systems of equations using Elimination:
-3x - 24y = -66
3x + 4y = -14
(-10, 4)
400
Find the Equilibrium Point for the demand and supply equations.
P = 500 - 0.4x
P = 380 + 0.1 xWhat is (240, 404)?
400
When enough units have been sold so that the total revenue R equals the total cost C.
What is the break-even point?
500
Solve the system graphically.
2x + y < 4
2x - y > 0
X > 0
500
Two numbers have a sum of 117. The larger number is 42 less than twice the smaller number.
What are the numbers.
What is the larger number is 64 and the smaller number is 53?
500
Solve
4x -2y + z=13
3x -y +2z= 13
x+ 3y -3z=-10
(2, -1, 3)
500
A total of $12,000 is invested in two funds paying 5% and 3% simple interest. The annual interest is $500.
How much is invested at each rate?
What is $7000 is invested at 5% and $5000 is invested at 3%?
500
Georgia bought 3 pens and 4 notebooks for $26.50 from the bookstore. She later bought 7 pens and 5 notebooks for $41.25 from the same bookstore. How much would you have to pay for 2 pens and 2 notebooks?
Pens $2.50 each
Notebooks $4.75 each
$14.50