Solving by Graphing
Substitution: Infinitely Many, One, or No Solution?
More: Infinitely Many, One, or No Solution?
Random
Context
100
What is the solution?
(-1,1)
100
Solve the systems of equations:
-3x + 4y = -2
y = -5
(-6, -5)
100
Solve the systems of equations:
14x + 2y = 26
-14x - 6y = -50
(1, 6)
100
What is it called when you have 2 or more equations with 2 or more variables?
A system of equations
100
Bo went to the grocery store and bought bottles of soda and bottles of juice. Each bottle of soda has 50 grams of sugar and each bottle of juice has 25 grams of sugar. Bo purchased a total of 7 bottles of juice and soda which collectively contain 250 grams of sugar. Determine the number of bottles of soda purchased and the number of bottles of juice purchased.
3 sodas, 4 juices
200
Solve using Graphing
y= 2x + 1
y= -x + 7
(2, 5)
200
Solve the systems of equations:
-5x - 5y = 10
y = -4x -17
(-5, 3)
200
Solve the systems of equations:
x -3y = 6
x + 3y = 12
(9,1)
200
What would a system of equations with infinite solutions look like on a graph?
One line.
200
Melanie is raising money for a school trip by selling candy bars and bags of chips. The price of each candy bar is $1.50 and the price of each bag of chips is $1.25. Yesterday Melanie made $33.25 and sold 13 more candy bars than bags of chips. Determine the number of candy bars sold and the number of bags of chips sold.
18 candy bars
5 bags of chips
300
Solve Using Graphing:
y = 5/3x + 2
y = -3
300
Solve the systems of equations:
y = -2x - 9
3x -6y = 9
(-3, -3)
300
Solve the systems of equations:
-6x - 10y = 4
6x + 10y = 0
No Solution
300
What would a system of equations with one solution look like on a graph?
Two lines that intersect at one point.
300
Morgan runs a farm stand that sells apples and blueberries. Yesterday Morgan sold 20 pounds of apples and 50 pounds of blueberries for a total revenue of $160. Today she sold 38 pounds of apples and 10 pounds of blueberries for a total revenue of $134.
What do your variables represent in this problem?
x = the price per pound of apples
y = the price per pound of blueberries
400
How many solutions are there?
Infinitely Many Solutions
400
Solve the systems of equations:
-8x - 5y = -24
-x + y = 10
(-2, 8)
400
Solve the systems of equations:
-3x - 24y = -66
3x + 4y = -14
(-10, 4)
400
Solve the following System of Equations using ANY method:
x = 3y - 5
2x - 3y = -4
(1, 2)
400
Alexa has $4.75 worth of dimes and quarters. She has 2 more dimes than quarters. Determine the number of dimes and the number of quarters that Alexa has.
15 dimes
13 quarters
500
Solve the systems of linear equations by graphing:
500
Solve the systems of equations:
-8x + y = -7
16x - 2y = 14
Infinitely Many Solutions
500
Solve the systems of equations:
-15x + 6y = -36
4x - 3y = 11
(2, -1)
500
What would a systems of equations with no solution look like on a graph?
Parallel Lines
500
Salma has set up a lemonade stand outside her house and sells small cups and large cups of lemonade. Each small cup holds 12 ounces of lemonade and each large cup holds 16 ounces of lemonade. Salma sold 60 cups of lemonade totaling 920 ounces. Determine the number of small cups sold and the number of large cups sold.
10 small
50 large