Solving Systems
Solve the following system of equations:
3x+2y=10
y=2x+5
Write your answer as an ordered pair!
(0,5)
A school holds a dance. The tickets cost $3 per person or $5 per couple. $475 worth of tickets are sold and 180 people attended the dance. Set up equations to find how many individuals and how many couples attended. (DO NOT SOLVE)
3p+5c=475
p+2c=180
Write an exponential equation given the following information:
Multiplier of 4.
Point at (0,9)
y=9(4x)
Name the best method to find the intersection point for the following system. Explain why.
y=x+7
y=2x-3
Equal values, both equations are y=.
We want to use substitution to solve the following system:
y=2x+5
3x+2y=10
Should we substitute for x or y?
y
Solve the following system of equations:
y=x-3
y=3x+7
Write your answer as an ordered pair!
(-5,-8)
The Frosty Ice-Cream Shop sells sundaes for $2 and banana splits for $3. On a hot summer day, the shop sold 8 more sundaes than banana splits and made $156. Set up equations to solve for how many sundaes and banana splits were sold. (DO NOT SOLVE)
2s+3b=156
b+8=s
Write an exponential equation given the following information:
Points at (0,9) and (1,81)
y=9(9x)
Name the best method to find the intersection point for the following system. Explain why.
x=2y-6
2x+6y=12
Substitution, One equation is x=, we can use that to substitute in for x.
We want to use equal values to solve the following system:
y=10x+12
2y=50x+40
What would be the first step to do this?
Divide by 2 on the bottom equation to get y by itself.
Solve the following system of equations:
3x+2y=12
2x-y=15
Write your answer as an ordered pair!
At a restaurant the cost for a breakfast taco and a small glass of milk is $2.10. The cost for 2 tacos and 3 small glasses of milk is $5.15. Which pair of equations can be used to determine t, the cost of a taco, and m, the cost of a small glass of milk? (DO NOT SOLVE)
t+m = 2.10
2t+3m = 5.15
Write an exponential equation given the following information:
Points at (1,12) and (2,48)
y=3(4x)
Name the best method to find the intersection point for the following system. Explain why.
2y+3x=10
-3x-5y=30
Elimination, If you add the systems, x will be eliminated.
We want to use elimination to solve the following system:
3x+2y=7
2x-10y=13
What be the first step to doing this?
Multiply the top equation by 5 so we can eliminate y.
Solve the following system of equations:
8x+7=y
2x-4y=14
Write your answer as an ordered pair!
(-1.4,-4.2)
Mr. White buys switch games and Xbox games. Switch games cost $50 while Xbox games cost $70. He has spent a total of $920 on the games. He owns 16 more switch games than Xbox games.
How many of each type does he have?
1 Xbox games and 17 Switch Games
Given the system of inequalities:
y≤x+2
y> 2x-3
Explain whether each line would be solid or dashed and whether you would shade above or below.
y≤x+2: Solid, shade below
y> 2x-3: Dashed, shade above
x=4+2y
y=12x+4
Substitution, You can substitute for either x or y because both equations are in x= or y= form.
We want to use elimination to solve the following system:
-2x+2y=10
x-8y=40
There are multiple ways to start. Name two of them.
Multiply the top equation by 4 so y is eliminated. Multiply the bottom equation by 2 so x is eliminated.
Solve the following system of equations:
100x+20y=500
30y-10x=150
Write your answer as an ordered pair!
(3.75, 6.25)
The difference of two numbers is 16. The bigger number is 5 less than 4 times the smaller number. Find the two numbers.
The two numbers are 23 and 7.
Given the system of inequalities:
y≤-x+2
y> 5x-3
Explain whether (5,7) and (0,1) are in the solution set.
(5,7) is not while (0,1) is.
Name the best method to find the intersection point for the following system. Explain why.
2x+y=300
3x-40=y
12y+6x=10
Desmos, We haven't solved three systems before :)
We want to use substitution to solve the following system:
3x=6y-9
2y=4x+10
There are multiple way's to start this. Name two of them.
Divide by three in the first equation to substitute for x. Divide by two in the second equation to substitute for y.