Substitution and Elimination
Using the Elimination method, solve:
-5x-8y=17
2x-7y=-17
X = -5
Y = 1
Using the Algebraic Method, Solve:
-7x-27=-36
-42x+4y=-152
X = 20/7
Y = 8
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?
202 Adult tickets were sold
346 Kids tickets were sold
The coach of a cricket team buys 7 bats and 6 balls for $3800. Later, she buys 3 bats and 5 balls for $1750. Find the cost of each bat and each ball.
The cost of each bat is $500
The cost of each ball is $50.
State whether each system of linear equations is inconsistent or has a unique solution.
x-y=14
4y=5+2x
Inconsistent
Using the Elimination method, solve:
-5x+y=-7
-3x-2=-12
X = 2
Y = 3
Using the Algebraic method Solve:
-x-37y=-1
-4x+6y=-22
X = 4
Y = -1
Eileen saves dimes and quarters she has 40 coins which totaled 6.55 in her bank how many of each coin does she have?
23 dimes and 17 quarters
Complete the tables of values for the system of linear equations:
X+Y=6 2x+y=8
X|0|1|2 X|0|1|2
Y|6|?|? Y|?|6|?
In the first table - bottom row - 6,5,4
in the second table - bottom row - 8,6,4
State whether each system of linear equations is inconsistent, dependent, or unique. Solve each system of linear equations if possible.
9x+21y=27
6x+14y=18
Dependent
Using the elimination method, solve:
5x-7y=-1
x-y=3
X = 6/5
Y = -9/5
Using the Algebraic method Solve:
-6x-y=23
12x-6y=-102
X = -5
Y = 7
Sum of the cost price of two products is $50. Sum of the selling price of the same two products is $52. If one is sold at 20% profit and other one is sold at 20% loss, find the cost price of each product.
The cost prices of two products are $30 and $20.
Graph x+y=6 and 2x+y=8 on the same coordinate point of intersection. Then use the graph to solve the systems of linear equations.
X=2
Y=4
David said he bought 9 apples and 6 apricots for $8.50 yesterday and bought 3 apples and 2 apricots for $7.40 today.
a) Write a system of equations to find the cost of an apple and an apricot.
b) State whether the system of linear equations has a unique solution, is inconsistent, or is dependent.
a) 9x+6y=8.5
3x+2y=7.4
b) Inconsistent
Using the substitution method solve:
3x+4y=6
x-2y=-6
x = 4
y = 3
Using the Algebraic Method Solve:
2x+y=0
2x-y=1
X = 1/4
Y = -1/2
Hannah paid $2.75 for 4 granola bars and 1 apple. Evie paid $2.25 for 2 granola bars and 3 apples. find the cost of each granola bar and each apple.
1 granola bar = $0.60
1 apple = $0.35
Solve using the graphical method:
y=2x-4
y=-1/3x+3
(3,2)
State whether each system of linear equations is inconsistent or dependent.
4x-7y=-29
2x+y=21
Unique
Solve using the substitution method:
x+y=5
x+2y=7
x = 3
y = 2
Hannah took her family to Nippo Lake to go golfing. There was a total of 15 people who went. The cost for a child to gold was $5 and the cost for an adult to gold is $10. She spent a total of $110. How many adults and kids went golfing?
X = # of kids
Y = # of adults
X = 8
Y = 7
The taxi charges in a city consist of a fixed charge together with the charge for the distance covered. For a distance of 10 km, the charge paid is $105 and for a journey of 15 km, the charge paid is $155. What are the fixed charge and charge per km? How much does a person have to pay for traveling a distance of 25 km?
The fixed charge is $5 and the charge per km for the distance covered is $10.
Solve using the graphical method:
3x-2y=-7
2x+y=7
(1,5)
State whether each system of linear equations is inconsistent, dependent, or unique.
x-y=6
5x+7y=-6
Unique