Solving Systems by Graphing
What does it mean if the system has one solution?
The lines are intersecting.
What are the steps for solving a system of equations using elimination method?
Make sure equations are lined up.
Get common coefficients if there aren't any.
Add or subtract the equations to eliminate the variable with common coefficients.
Solve for the remaining variable.
Plug in your answer and solve for the other variable.
What are the steps to solve a system of equations using substitution?
Solve one equation for x or y.
Substitute it into the other equation and solve.
Plug your answer back in and solve for the other variable.
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.
Solve this system by elimination.
4x - 2y = 12
y = 2x + 6
No solution
0 = 18
Solve the system by substitution.
2y = 4x + 8
8x - 4y = 16
No Solution
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 solution is infinite?
It is the same line.
What would the system look like after you eliminate the appropriate variable?
-3x + 2y = 8
3x -6y = 8
-4y = 16
Set up the following system of equations for substitution method:
x+4y=0
3x+2y=20
x=-4y
3x+2y=20
3(-4y)+2y=20
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
Solve the system using elimination.
4x - 2y = 14
-x - 2y = -6
(4, 1)
Is (-9,5) the correct solution for the system of equations:
x-3y=-24
5x+8y=-5
Yes! (-9,5) makes both equations true.
-9-3(5)=-24
-9-15=-24
5(-9)+8(5)=-5
-45+40=-5
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)
Solve the system using elimination:
2x - 6y =12
-5x+15y=-30
Infinite!
0=0
Free Points
Enjoy
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.