Solving Systems by Graphing
What does it mean if the system has one solution?
The lines are intersecting.
Jeopardy Picture 1
(3,1)
Solve the linear equation for x.
2x - 4y = -8
x = 2y - 4
Draw the system of inequalities on the grid side of your whiteboards.
y ≥ 2x - 1
x + 3y < 2
Draw your response.
If we defined x as pants and y as shirts when solving a word problem, then determined that (4,3) was in the solution area, how would you interpret that answer?
4 pants and 3 shirts
What does it mean if the system has no solution?
The lines are parallel.
Jeopardy Picture 2
(2, 4)
What is the slope of the line -6x + 2y = 8
m = 3
What inequality symbol tells you to use a dotted line?
What inequality symbol tells you to use a solid line?
Dotted: > or <
Solid: > or <
Mary and Haley went to a candy store. Mary bought 3 chocolate bars and 4 lollipops for $12.15. Haley bought 2 chocolate bars and 3 lollipops for $8.55. How much does one chocolate bar cost?
$1.35
What does it mean if the system has infinitely many solutions?
It is the same line.
Jeopardy Picture 3
(-6, -3)
If the slope of line A is 7, what is the slope of a line perpendicular to line A?
1/7
What inequality symbol tells you to shade above the line?
What inequality symbol tells you to shade below the line?
Above: > or >
Below: < or <
Give the equations for the following word problem:
Emily knits scarves and sweaters to sell. Scarves take 2 hours to knit, and sweaters take 10 hours. Emily would like to spend no more than 40 hours per week knitting at knit at least 5 items per week.
2x+10y < 40
x+y > 5
What are the settings needed to be changed in desmos?
1. Uncheck minor grid lines
2. Input 1 for both steps
Jeopardy Picture 4
No Solution
On the grid side of your whiteboards, draw the inequality below.
y - 4 ≤ 0
Draw your answer.
How do you determine the solutions for a system of linear inequalities?
The double shaded area (and on the solid line in the double shaded area).
Jamie needs new shoes for vacation. She wants a couple different options of sandals and sneakers. Sandals cost $17.99 and sneakers cost $23.99. She can spend no more than $170 on the shoes. Write a linear inequality to represent the number of sandals (x), and the number of sneakers (y) that she can purchase.
17.99x + 23.99y ≤ 170
On the grid side of your whiteboards, draw a graph to show the solution for the system:
y= -x + 3
y= x - 1
(2,1)
Jeopardy Picture 5
Infinite Solutions
Write the inequality for the graph in Jeopardy Picture 6.
x - 2y > 8
or
y < 1/2 x - 4
Provide 3 solutions to the following system of inequalities.
2x + 3y ≥ 5
4x - 3y > 3
Multiple answers.
Cameron received a $25.00 gift card to an online retailer that sells music and games. Each song costs $0.89 and each game costs $1.99. He wants to buy at least 15 items with his gift card.
Set up a system of inequalities that represents this scenario.
Provide 3 possible combinations of songs and games that Cameron can purchase.
Multiple answers.