Question

solve the following equation by Substitution method 2x+3y = 11
2x- 4y=24​

Answer 1

Answer:

Value of x is 58/7and y is -13/7 .

Step-by-step explanation:

We have equations :

• 2x + 3y = 11

• 2x - 4y = 24

Let equations be :

• 2x + 3y = 11 ----------(i)

• 2x - 4y = 24 ---------(ii)

Take equation (ii) :

→ 2x - 4y = 24

→ 2x = 24 + 4y

→ x = (24 + 4y)/2

→ x = 24/2 + 4y/2

→ x = 12 + 2y --------(iii)

Put value of x in equation (i) :

→ 2x + 3y = 11

→ 2 × (12 + 2y) + 3y = 11

→ 24 + 4y + 3y = 11

→ 24 + 7y = 11

→ 7y = 11 - 24

→ 7y = - 13

→ y = -13/7

Now, Put value of y in any equation for value of x:

→ x = 12 + 2y ----------(iii)

→ x = 12 + 2 × (-13/7)

→ x = 12 - 26/7

→ x = (84 - 26)/7

→ x = 58/7

Thus,

Value of x is 58/7 and y is -13/7 .

Answer 2

Answer:

❒ Given :-

➲ 2x + 3y = 11

➲ 2x - 4y = 24

❒ To Find :-

● What is the value of x and y.

❒ Method Used :-

● Substitution Method.

Solution :-

Given Equation :

$\mapsto \sf\bold{\purple{2x + 3y =\: 11\: ------\: (Equation\: No\: 1)}}$

$\mapsto \sf\bold{\purple{2x - 4y =\: 24\: ------\: (Equation\: No\: 2)}}$

From the equation no 2 we get,

$\implies \bf 2x - 4y =\: 24$

$\implies \sf 2x =\: 24 + 4y$

$\implies \sf x =\: \dfrac{24 + 4y}{2}$

$\implies \sf x =\: \dfrac{\cancel{24} + \cancel{4}y}{\cancel{2}}$

$\implies \sf x =\: \dfrac{12 + 2y}{1}$

$\implies \sf\bold{\purple{x =\: 12 + 2y\: ------\: (Equation\: No\: 3)}}$

Now, by putting x = 12 + 2y in the equation no 1 we get,

$\implies \sf 2x + 3y =\: 11$

$\implies \sf 2(12 + 2y) + 3y =\: 11$

$\implies \sf 2(12) + 2(2y) + 3y =\: 11$

$\implies \sf (2 \times 12) + (2 \times 2y) + 3y =\: 11$

$\implies \sf 24 + 4y + 3y =\: 11$

$\implies \sf 24 + 7y =\: 11$

$\implies \sf 7y =\: 11 - 24$

$\implies \sf 7y =\: - 13$

$\implies \sf\bold{\blue{y =\: \dfrac{- 13}{7}}}$

Again, by putting the value of y in the equation no 2 we get,

$\implies \sf 2x - 4y =\: 24$

$\implies \sf 2x - 4\bigg(\dfrac{- 13}{7}\bigg) =\: 24$

$\implies \sf 2x + \dfrac{52}{7} =\: 24$

$\implies \sf 2x =\: 24 - \dfrac{52}{7}$

$\implies \sf 2x =\: \dfrac{168 - 52}{7}$

$\implies \sf 2x =\: \dfrac{116}{7}$

$\implies \sf x =\: \dfrac{116}{7} \times \dfrac{1}{2}$

$\implies \sf x =\: \dfrac{116 \times 1}{7 \times 2}$

$\implies \sf x =\: \dfrac{\cancel{116}}{\cancel{14}}$

$\implies \sf\bold{\blue{x =\: \dfrac{58}{7}}}$

Hence, the value of x and y will be :

$\bigstar\: \: \sf\bold{\red{The\: value\: of\: x =\: \dfrac{58}{7}}}$

$\bigstar\: \: \sf\bold{\red{The\: value\: of\: y =\: \dfrac{- 13}{7}}}$

${\small{\bold{\underline{\therefore\: The\: value\: of\: x\: is\: \dfrac{58}{7}\: and\: the\: value\: of\: y\: is\: \dfrac{- 13}{7}\: .}}}}$