# SOLVING SYSTEMS OF EQUATIONS USING CRAMERS RULE WORKSHEET

Solving Systems of Equations Using Cramers Rule Worksheet :

Here we are going to see some example problems of solving linear equations by crammer's rule.

## Solving Systems of Equations Using Cramers Rule Worksheet - Examples

(1) Solve the following systems of linear equations by Cramer’s rule:

(i)  5x − 2y + 16 = 0, x + 3y − 7 = 0        Solution

(ii)  (3/x) + 2y  =  12, (2/x) + 3y  =  13       Solution

(iii)  3x + 3y − z =11, 2x − y + 2z = 9, 4x + 3y + 2z = 25

(iv)  (3/x) - (4/y) - (2/z) - 1  =  0

(1/x) + (2/y) + (1/z) - 2  =  0

(2/x) - (5/y) - (4/z) + 1  =  0             Solution

(2)  In a competitive examination, one mark is awarded for every correct answer while 1/4 mark is deducted for every wrong answer. A student answered 100 questions and got 80 marks. How many questions did he answer correctly ? (Use Cramer’s rule to solve the problem)

Solution

(3)  A chemist has one solution which is 50% acid and another solution which is 25% acid. How much each should be mixed to make 10 litres of a 40% acid solution ? (Use Cramer’s rule to solve the problem).          Solution

(4)  A fish tank can be filled in 10 minutes using both pumps A and B simultaneously. However, pump B can pump water in or out at the same rate. If pump B is inadvertently run in reverse, then the tank will be filled in 30 minutes. How long would it take each pump to fill the tank by itself ? (Use Cramer’s rule to solve the problem).

Solution

(5)  A family of 3 people went out for dinner in a restaurant. The cost of two dosai, three idlies and two vadais is  150. The cost of the two dosai, two idlies and four vadais is 200. The cost of five dosai, four idlies and two vadais is 250. The family has 350 in hand and they ate 3 dosai and six idlies and six vadais. Will they be able to manage to pay the bill within the amount they had ?

After having gone through the stuff given above, we hope that the students would have understood, "Solving Systems of Equations Using Cramers Rule Worksheet".

Apart from the stuff given in this section "Solving Systems of Equations Using Cramers Rule Worksheet"if you need any other stuff in math, please use our google custom search here.

You can also visit our following web pages on different stuff in math.

WORD PROBLEMS

Word problems on simple equations

Word problems on linear equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

Word problems on comparing rates

Converting customary units word problems

Converting metric units word problems

Word problems on simple interest

Word problems on compound interest

Word problems on types of angles

Complementary and supplementary angles word problems

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed

Word problems on sum of the angles of a triangle is 180 degree

OTHER TOPICS

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6