Question

guies pls solve no 19 i request u plz
THIS IS OF CHAPTER LINEAR EQUATIONS IN TWO VARIABLE​

Answer 1

This is a simple question;

Let's have a look in this question;

Question;

9 chairs and 5 tables cost ₹90, while 5 chairs and 4 tables cost ₹61. Find the price of 6 chairs and 3 tables.

So, before we start solving this question, let's take 2 variables;

Let's take x for chair, and y for table;

So, now let's write the question again, but in the form of 2 equations;

Equation 1 : 9x + 5y = 90

Equation 2 : 5x + 4y = 61

So, as we have these 2 equation, and we have to find the values of x and y;

Let's use Substitution Method;

9x + 5y = 90

⇒ 9x = 90 - 5y

⇒ x = $\dfrac{90 - 5\text{y}}{9}$     ....(3)

Let's substitute the value of x in the Equation 2;

5x + 4y = 61

⇒ 5 × $\dfrac{90 - 5\text{y}}{9}$ + 4y = 61

Now, let's simplify the above equation;

⇒ $\dfrac{5(90 - 5\text{y})}{9} + 4\text{y} = 61$

⇒ $\dfrac{5(90 - 5\text{y})}{9} + \dfrac{9(4\text{y})}{9} = 61$

⇒ $\dfrac{450 - 25\text{y}}{9} + \dfrac{36\text{y}}{9} = 61$

⇒ $\dfrac{450 - 25\text{y}+36\text{y}}{9}= 61$

Simplify;

$\dfrac{450 + 11\text{y}}{9}= 61$

Now, multiply both sides by 9;

$\dfrac{450 + 11\text{y}}{\cancel{9}}\times\cancel{9}= 61\times9$

Simplify;

$450 + 11\text{y}= 549$

Now, Subtract 450 from both sides;

$\cancel{450} + 11\text{y} \cancel{- 450}= 549 - 450$

Simplify;

$11\text{y}= 99$

Now, divide 11 from both sides;

$\dfrac{\cancel{11}\text{y}}{\cancel{11}}= \dfrac{99}{11}$

Simplify;

y = 9

Now, put the value of y in the Equation 3;

x = $\dfrac{90 - 5\text{y}}{9}$

⇒ x = $\dfrac{90 - 5\text{y}}{9}$

      = $\dfrac{90 - 5\times9}{9}$

Simplify;

$\text{x}=\dfrac{90 - 45}{9}$

⇒ $\text{x}=\dfrac{45}{9}$

⇒ x = 5

Now as we have found the values of x and y; Let's put these values in the Equation 6x + 3y = z.

*Here z is a variable for the cost, or the price.*

6(5) + 3(9) = z

Get rid of the parenthesis;

30 + 27 = z

Simplify;

57 = z

Therefore, the cost of 6 chairs and 3 tables is ₹57.