Systems of linear equations

By Comenius group of PGU, Germany

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

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?

Solution:bakery

Bread xRoll y3x+5y= 4,105x+2y= 5,80  3x+5y= 4,10 /-5y3x= 4,10-5y /:3x = 1,37-1,67y 5x+2y= 5,80 /T6,85-8,35y+2y= 5,80 /T6,85-6,35y= 5,80 /-6,85-6,85y= -1,05 /:6,85-y=-0,153 /*(-1)y=ca. 0,153 euro 3x+5y=4,10 /T3x+0,765=4,10 /-0,7653x=3,34 /:3x= ca. 1,11 euro

Icehockey in BelarusIt’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)?

Solution:Icehockey in Belarus

a)2340x + 780y = 50700 |-2340x 780y = 50700 – 2340x |:780y = 65 – 3x2520x + 360y = 51480 |-2520x360y = 51480 – 2520x |:360y = 143 – 7x65 – 3x = 143 – 7x |+7x65 + 4x = 143 |+654x = 78 |:4x = 19,5y = 6,5 Answer: An adult have to pay 19,5€ and a child have to pay 6,5€.b)First game:2340 + 780 = 31203120 = 100 %31,2 = 1 %780 : 31,2 = 25 %Second game: 2520 + 360 = 28802880 = 100%28,8 = 1%360 : 28,8 = 12,5%

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?

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?