Simple and Linear Equations - One Two and Three Variables Explained with Examples

In this video I have explained the basics of Simple and Linear Equations. Linear Equations are those equations which have the maximum degree of any variable as unity. A soon as the degree of any variable becomes more than one it becomes a polynomial and then it comes under the topic of Algebra. In Linear Equations we have different number of variables. From the viewpoint of competitive exam preparation equations involving one two and three variables are generally asked and we will cover all three of them in detail with examples and specific types of questions that are asked in examinations. First of all I have explained the case of one unknown in one equation involving one variable. After that two unknown involving two equations having two variables each have been solved by me for beginners who want to learn the way of solving them. The equations solved by me as as follows -

2x + 3y = 8 and 5x + 4y = 13

After this I have solved some questions which are listed below -

Question 1. Four mobile phones and three tablets cost Rs. 94,000, while six mobile phones and eight tablets together cost Rs. 1,62,000. Find the cost of one mobile phone and one tablet ?

Question 2. 33 pencils and 47 erasers together cost Rs. 299, while 47 pencils and 33 erasers cost Rs. 341. Find the cost of a pencil and an eraser ?

Question 3. The sum of a digits of a two digit number is 8. The difference between this number and the number obtained by reversing the digits is 18. Find the two digit number ?

Question 4. The ages in years of Ram and Shyam are in the ratio of 5:7. If Ram were 9 years older and Shyam 9 years younger, the age of Ram would have been twice the age of Shyam. Find their ages?

Question 5. The sum of the ages of the father and his son is 54 years. After 18 years, father will be twice as old as his son. Find their present ages ?

Question 6. Monica ordered for six parker pens and some additional Reynolds pen. The price of Parker pen is 2.5 times that of Reynolds pen. While preparing the bill, the shopkeeper interchanged the number of Parker pens will Reynolds pen, which increased the amount of the bill by 45 percent. Find the number of Reynolds Pen ?

Now I have solved the below three equations to show you how three equations having three variables each are solved.

6x + 2y + 4z = 16 and 5x + 3y + z= 13.5 and 4x + 3y + 3z = 12.5

Then I have discussed a special case involving two equations having three variables each and then have explained the conditions under which we would be able to calculate the exact value of one of those variables. Questions based on three variables discussed by me in this video are listed below -

Question 7. Two pencils, three erasers and four sharpeners cost Rs. 46. Three pencils, one eraser and six sharpeners cost Rs. 62. Find the cost of one eraser ?

Question 8. Ram and Shyam went to a bakery shop. Ram ate four puffs, 3 burgers and 2 cakes and used up all the money he had. Shyam ate three puffs, 6 burgers and 4 cakes and paid an amount which is 25 percent more than what Ram paid. What percentage of Ram's money was spent on the puffs he ate ?