Solving Using Graphs
What is the solution of the system?
Line 1: m = -2, b = 4
Line 2: m = 1, b = -5
(3,-2)
How many solutions does this system have?
y = 4x - 9
y - 4x = 6
No solution- parallel lines
What is the solution of the system? Use elimination. 2x - 3y = -12
3x - 2y = 2
(6, 8)
Is the ordered pair a solution of the linear inequality?
3y > 5x -12; (-6, 1)
yes
What method of solving do you use when one equation is already solved for one of the variables, or when it is easy to solve for one of the variables?
Substitution
What is the solution:
3y= x - 2
-6y=-2x + 4
Infinitely many solutions
What is the solution of the system using substitution?
y= 5x
x+y= 12
(2, 10)
What is the solution of the system? Use elimination. -2x + 12y = -30
3x - 4y = 17
(3, -2)
What is the inequality that represents the graph?
y > -4/3 + 5
A carpenter makes and sells rocking chairs. The material for each chair costs $22.50. The chairs sell for $75 each. If the carpenter spends $420 on advertising, how many chairs must she sell to break even?
8
Find the solution by graphing:
y= 1/2x + 7
y= 2/3x + 3
(4, 9)
What is the solution to the system using substitution?
7x - 3y = 2
-2y + x = -6
(2, 4)
If you add two equations in two variables and the sum is an equation in one variable, what method are you using to solve the system?
Elimination
Is the ordered pair a solution of the system?
y > 2x + 4
y < 3x + 7 (2, 12)
Yes
What method should you use to solve is you want a visual display of the equations, or when to estimate a solution?
Graphing
What is the solution of two lines that have the same slope?
No solution- parallel lines
The school bookstore sells T-shirts for $8 and sweatshirts for $12. Last month, the bookstore sold 37 T-shirts and sweatshirts for a total of $376. How many T-shirts were sold?
17
How many solutions foes the system have?
12x - 8y = 20
3x - 2y = 5
infinitely many
What is the graph of the inequality?
y < x - 1
check graphs
Dylan is filling a 20- gallon tank and a 30- gallon tank for his fish display. The 20- gallon tank contains 4 gallons of water and is filled at a constant rate of 10 gallons per hour. The 30- gallon tank contains 13 gallons of water and is fulled at a constant rate of 7 gallons per hour. When will the two tanks have the same amount of water?
NEVER
Solve the system by graphing:
2x - y = -5
-2x - y = -1
(-1, 3)
True or False? Explain. When solving a system using substitution, if you obtain 0 = 0, then the system has no solution.
False- it has infinitely many solutions
The theater club sells a total of 101 tickets to its first play. A student ticket costs $1. An adult ticket costs $2.50. Total ticket sales are $164. How many student tickets were sold?
59
What is the graph of the system?
y > or equal to 2x - 1
x + y < 2
check graphs
How many solutions does a system have if the lines have the same slope and y- intercept?
infinitely many solutions