Question

Define a linear equation. Write its general form. Also, describe applications of linear equations.​

Answer 1

Answer:

Hi friends

Step-by-step explanation:

The standard form for linear equations in two variables is Ax+By=C. For example, 2x+3y=5 is a linear equation in standard form. When an equation is given in this form, it's pretty easy to find both intercepts (x and y).

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Answer 2

A linear equation is an equation that is written for two different variables. This equation will be a linear combination of these two variables, and a constant can be present. Surprisingly, when any linear equation is plotted on a graph, it will necessarily produce a straight line - hence the name: Linear equations.

________________Applications___________

If 2 is added to the numerator and denominator it becomes 9/10 and if 3 is subtracted from the numerator and denominator it become 4/5. Find the fractions.

Solution:

Let the fraction be x/y.

If 2 is added to the numerator and denominator fraction becomes 9/10 so, we have

(x + 2)/(y + 2) = 9/10

or, 10(x + 2) = 9(y + 2)

or, 10x + 20 = 9y + 18

or, 10x – 9y + 20 = 9y – 9y + 18

or, 10x – 9x + 20 – 20 = 18 – 20

or, 10x – 9y = -2 ………. (i)

If 3 is subtracted from numerator and denominator the fraction becomes 4/5 so, we have

(x – 3)/(y – 3) = 4/5

or, 5(x – 3) = 4(y – 3)

or, 5x – 15 = 4y – 12

or, 5x – 4y – 15 = 4y – 4y – 12

or, 5x – 4y – 15 + 15 = – 12 + 15

or, 5x – 4y = 3 ………. (ii)

So, we have 10x – 9y = – 2 ………. (iii)

and 5x – 4y = 3 ………. (iv)

Multiplying both sided of equation (iv) by 2, we get

10x – 8y = 6 ………. (v)

Now, solving equation (iii) and (v) , we get

10x – 9y = -2

10x – 8y = 6

- y = - 8

y = 8

Substituting the value of y in equation (iv)

5x – 4 × (8) = 3

5x – 32 = 3

5x – 32 + 32 = 3 + 32

5x = 35

x = 35/5

x = 7

Therefore, fraction becomes 7/8.

________________Practice Sums________

Problem 1 :

Raman’s age is three times he sum of the ages of his two sons. After 5 years his age will be twice the sum of the ages of his two sons. Find the age of Raman

Problem 2 :

The middle digit of a number between 100 and 1000 is zero and the sum of the other digit is 13. If the digits are reversed, the number so formed exceeds the original number by 495. Find the number

Answers to the practice suns are in the attachment (:

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