Substitution
Elimination
Situations
Solving Equations
Mixed Review
100
Solve using substitution:
y=x+2
x=−3
(−3, −1)
100
Solve using elimination:
3x−y=17
−x+y=−7
(5,–2)
100
Describe how to find the solution to a system from a graph and a table
On a graph the solution is where the lines intersect.
A table means both equations have the same x and y values
100
Solve for y:
y-2x=10
y=2x+10
100
Estimate the solution from the graph.
x= 1.125 to 1.333
y=2.125 to 2.333
200
Solve using substitution:
y=4x+10
y=2x+12
(1,14)
200
Solve using elimination:
x+y=5
2y−x=−2
(4, 1)
200
Write a system for the situation
Mr. Williams is hosting a lap-a-thon. So far Drew has raised $20 and earns $2 for every lap he runs. Ali has $10 and earns $5 for every lap she runs.
y=20+2x
y=10+5x
200
Solve for b:
t=an+b
t−an=b
200
(4, 5) (6, 10)
What is the slope?
m = 2/5
300
Solve using substitution:
y=2x+1
2y+3x=16
(2,5)
300
Solve using elimination:
2x+y=10
3x−2y=1
(3, 4)
300
Solve:
Kevin has $20 and earns $4 per hour babysitting
Ian has $5 and earns $7 babysitting.
When will they have the same money and how much?
After 5 hours they both have $40
300
4y−2(6−y)=6
y=3
300
If the slope is 3 and a point on the line is (1, 7) what is b?
y=3x+b
b=4
400
y=4x+10
y=2x+12
Is (3, 22) a solution? explain your reasoning
No because doesn't work for the second equation
400
Solve using elimination:
(10, 2)
400
Write a system for the situation:
A park charges $10 for adults and $5 for kids. How many many adults tickets and kids tickets were sold, if a total of 548 tickets were sold for a total of $3750 ?
10a+5k=3750
a+k=548
400
Solve for m:
m = –12
400
What is the explicit form
an=an+1+7
a1=5
an=7n-2
500
Write a system of equations that fits the situation:
There are a total of 55 points scored in a football game. You get 7 points for a touchdown and 3 points for a field goal. The number of field goals is one more than twice the number of touchdowns. How many field goals and touchdowns were there?
f=1+2t
55=7t+3f
500
Write a system of equations that fits the situation:
There are 21 animals on Farmer Cole’s farm—all sheep and chickens. If the animals have a total of 56 legs, how many of each type of animal lives on his farm?
Bonus points for solving accurately.
c+s=21
2c+4s=56
Chickens: 14
Sheep: 7
500
Write a system for the situation:
A large pizza at Palanzio’s Pizzeria costs $6.80 plus $0.90 for each topping. The cost of a large cheese pizza at Guido’s Pizza is $7.30 plus $0.65 for each topping. How many toppings need to be added to a large cheese pizza from Palanzio’s Pizzeria and Guido’s Pizza in order for the pizzas to cost the same, not including tax?
y=6.80+.90x
y=7.30+.65x
500
Solve for x:
(x−3)(x+4)=x2+4
x=16
500
If the slope of a line is 2 and a point on the line is (3, 7) what is the y-intercept (b)?
y=2x+b
b=1