Identifying Solutions
Solving by Graphing
Solving by Substitution
Solving By Elimination
Word Problems
100
What are the steps to identify a solution to a system?
Plug the ordered pair into the equations, if the ordered pair works for both equations then the ordered pair is a solution to the systems.
100
Find the solution to the System of Equations
(1,3)
100
Solve by substitution.
y= 12-3x and
y=2x-3
(3,3)
100
Solve the following system by elimination
x+3y=-7 and -x+2y=-8
(2,-3)
100
Solve using elimination: Brianna’s family spent $134 on 2 adult tickets and 3 youth tickets at an amusement park. Max’s family spent $146 on 3 adult tickets and 2 youth tickets. What is the price of a youth ticket? Write the equations as well.
2x+3y=134 and 3x+2y=146;
$22 for a youth ticket.
200
Is the following ordered pair a solution to the given equations?
(7,8) 7x+3y=24
3x+5y=14
No.
200
Find the solution for the following equations.
y=x-1
y=2x+2
Answer:
200
Solve the following equations by substitution.
3x-2y=-3 AND y=7-4x
(1,3)
200
Solve the Following system by elimination.
x+3y=-4 and 2x-4y=32
(8,-4)
200
Mr. Malone is putting money in two savings accounts. Account A started with $200 and Account B started with
$300. Mr. Malone deposits $15 in Account A and $10 in Account B each month. In how many months will the
accounts have the same balance? What will that balance be?
In 20 months the balance would be $500 in each account.
300
Is the following ordered pair a solution to the equations?
15x+27y=48
5x+9y=16
(1.4,1)
Bonus: 300 points
How many solution(s) do the above equations have?
Yes
Bonus Answer: Infinitely many solutions
300
What is the solution to the following equations? Draw a graph.
-5/3x+3=y
1/3x-3=y
300
Solve the equations using substitution
4y-2x=-2 and x+3y=-4
(-1,-1)
300
Solve the systems of equation using elimination.
-10x+y=0 and 5x+3y=-7
(-0.2,-2)
300
Solve by Substitution.
Kate bought 3 used CDs and 1 used
DVD at the bookstore. Her friend Joel
bought 2 used CDs and 2 used DVDs at
the same store. If Kate spent $20 and
Joel spent $22, determine the cost of a
used CD and a used DVD.
A used CD costs $4.50
A used DVD costs $6.50
400
Is the ordered pair a solution to the system?
(1,3)
2x - 3y = -7
-5x + 3y = 4
Yes
400
Given the graph and the solution write the corrrect equations. Solution: (-2,1)
y=1/2x+2, y=2x-3
400
Find the solution of the equations by substitution.
3y+6x=9 and
2(y+3)=-4x
no solution
400
Solve using elimination (although another way might be easier)
x+16.5=-0.75y and
y=0.5x
(-12,-6)
400
Solve using whichever method you want.
A car dealership has 378 cars on its lot. The ratio of new cars to used cars is 5:4. Write and solve a system of equations to find the number of new and used cars on the lot.
new cars - 190
used cars - 188
500
identify the system of equations:
3x + 2y = 7
-4x - 3y = 10
a) inconsistent - no solutions
b) independent - one solution
c) dependent - many solutions
What is b) independent - one solution
500
Based on the 2 equations given can you determine a solution? If yes, what is the solution? If not, what makes the lines not have a solution? And can you tell if the lines are consistent. inconsistent, dependent or independent?
y=2x-4,
y=2x+1
The Lines are parallel so there is no solution. The lines are inconsistent and the graph looks like this -->
500
Classify the system and find the solution, if there is one.
3x-13=2y and
-3y=2x
consistent, (3,-2)
500
Solve the system of equations using elimination.
2x+y+z=17
0.5z=5
x-y=5
x=4, y=-1. and z=10
If you got this question correct give yourself 1000 points.
500
Solve using whichever method you want.
The sum of the digits of a two-digit number is 5. If the number is multiplied by 3, the result is 42. Write and solve a system of equations to find the number. (Hint: One equation involves the digits in the number. The other equation involves the values of the digits.)
The number is 14.
The system is x+y=5 and 3(10x +y)=42. x=1 and y=4