systems of linear equations

1. Linear
Equations
By Comenius group of PGU, Germany

2. Some tasks
Here we have some tasks for solving
systems of linear equations.
We hope that it’s a help for the next class
test or other things. Some tasks haven’t got
solutions but we hope that isn’t a problem.
Comenius group from Germany

3. bakery
Yesterday I bought at the bakery three
breads and 5 rolls for 4,10 euros. Today I
bought 5 breads and 2 rolls for 5,80 euros.
O How expensive is one bread and one
roll?

4. Solution:
bakery
Bread x
Roll y
3x+5y= 4,10
5x+2y= 5,80
3x+5y= 4,10 /-5y
3x= 4,10-5y /:3
x = 1,37-1,67y
5x+2y= 5,80 /T
6,85-8,35y+2y= 5,80 /T
6,85-6,35y= 5,80 /-6,85
-6,85y= -1,05 /:6,85
-y=-0,153 /*(-1)
y=ca. 0,153 euro
3x+5y=4,10 /T
3x+0,765=4,10 /-0,765
3x=3,34 /:3
x= ca. 1,11 euro

5. Icehockey in Belarus
It’s icehockey worldchampionschip in Belarus. To the
first game, which was Germany against Russia, 2340
adults and 780 children came. The organisators
earned 50700€. The return match was watched by
2520 adults and 360 children. In that game they
earned 51480€.
O How much does an entrance ticket cost for an
adult and how much does a child have to pay?
O How many children were visiting the game (in
percent)?

6. Solution:
Icehockey in Belarus
a)2340x + 780y = 50700 |-2340x
780y = 50700 – 2340x |:780
y = 65 – 3x
2520x + 360y = 51480 |-2520x
360y = 51480 – 2520x |:360
y = 143 – 7x
65 – 3x = 143 – 7x |+7x
65 + 4x = 143 |+65
4x = 78 |:4
x = 19,5
y = 6,5
Answer: An adult have to pay 19,5€ and a child have to pay 6,5€.
b)First game:
2340 + 780 = 3120
3120 = 100 %
31,2 = 1 %
780 : 31,2 = 25 %
Second game:
2520 + 360 = 2880
2880 = 100%
28,8 = 1%
360 : 28,8 = 12,5%

7. The illegal Pokémon market
On the illegal market for Pokémon, a seller
sells only Charmanders and Charizards.
He sells 5 Charmanders and 8 Charizards
on one day. He gets 2525$ in total. The day
before he sold 12 Charmanders and 4
Charizards, so he earned 1500$.
O How much costs one of each
Pokémon?

8. A handball club
A handball club has two games. To the first
game came 1346 adult and 634 children.
They took 11324 euro for tickets of this
game. To the next game 2359 adults
cameand only the half of the children, who
came to the first game. They took 5.235.572
Euro from tickets.
O How much costs a ticket for an adult
and how much for a child?