Question

2x + 3y = 11
2x - 4y = -24{ method substitution }​

Answer 1

Step-by-step explanation:

Mark 2x + 3y = 11 as eq (i)

And 2x - 4y = - 24 as eq (ii)

Now from eq (i)

2x + 3y = 11

2x = 11 - 3y

Therefore, x = (11 - 3y)/2

Put the value of x in eq (ii)

Therefore, 2x - 3y = - 24

2((11 - 3y)/2) - 3y = - 24

(22 - 6y)/2 - 3y = - 24

(22 - 6y - 6y)/2 = - 24

22 - 12y = ( - 24)(2)

22 - 12y = - 48

11 - 6y = - 24 (taking 2 as common)

- 6y = - 24 - 11

- 6y = - 35

6y = 35 (negative sign on both sides)

Therefore, y = 35/6

Therefore, x = (11 - 3y)/2

= (11 - 3(35/6))/2

= (11 - 75/6)/2

= ((66-75)/6)/2

= ((66 - 75)(2))/2

= (( - 9)(2))/2

= - 18/2

= - 9

Therefore, x = - 9 and y = 35/6

HOPE THIS HELPS YOU THANK YOU

Answer 2

❒ Given :-

• 2x + 3y = 11
• 2x - 4y = 24

❒ To Find :-

• What is the value of x and y.

❒ Method Used :-

• Substitution Method.

Solution :-

Given Equation :

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

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

From the equation no 2 we get,

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

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

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

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

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

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

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 :

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

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

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