Question

Solve: x + y = 11 ; 2x - 3y = 7​

Answer 1

We know that -:

• x + y = 11 (i)
• 2x - 3y = 7 (ii)

Now we will find the value of 'x' in equation (i)

⇒ x + y = 11

⇒ x = 11 - y

We will now substitute the value of 'x' in equation (ii)

⇒ 2x - 3y = 7

⇒ 2 (11 - y) - 3y = 7

⇒ 2 (11) - 2 (y) - 3y = 7

⇒ 22 - 2y - 3y = 7

⇒ 22 - 5y = 7

⇒ -5y = 7 - 22

⇒ -5y = -15

⇒ y = 15 ÷ 5

⇒ y = 3

With the obtained value of 'y' we will find the value of 'x'.

⇒ x + y = 11

⇒ x = 11 - y

Let's substitute the value of 'y' in equation (i)

⇒ x = 11 - y

⇒ x = 11 - 3

⇒ x = 8

∴ x = 8

∴ y = 3

Answer 2

Step-by-step explanation:

Given:-

• x + y = 11.
• 2x - 3y = 7.

$\frak{\underline{\underline{\dag Let's\ find\ the\ value\ of\ "x"\ in\ equation(1):-}}}$

$\bf : \implies {x\ +\ y\ =\ 11} \\ \\ \bf : \implies {x\ =\ 11\ -\ y.}$

$\frak{\underline{\underline{\dag By\ substituting\ the\ value\ of\ "x"\ in\ equation(2):-}}}$

$\bf : \implies {2x\ -\ 3y\ =\ 7} \\ \\ \bf : \implies {2\ (11\ -\ y)\ -\ 3y\ =\ 7} \\ \\ \bf : \implies {2\ (11)\ -\ 2\ (y)\ -\ 3y\ =\ 7} \\ \\ \bf : \implies {22\ -\ 2y\ -\ 3y\ =\ 7} \\ \\ \bf : \implies {22\ -\ 5y\ =\ 7} \\ \\ \bf : \implies {-5y\ =\ 7\ -\ 22} \\ \\ \bf : \implies {-5y\ =\ -15} \\ \\ \bf : \implies {y\ =\ \cancel \dfrac{15}{5}} \\ \\ \bf : \implies {\purple{\underline{\boxed{\bf y\ =\ 3.}}}}\bigstar$

$\frak{\underline{\underline{\dag Now,\ finding\ the\ value\ of\ "x"\ with\ the\ value\ of\ "y":-}}}$

$\bf : \implies {x\ +\ y\ =\ 11} \\ \\ \bf : \implies {x\ =\ 11\ -\ y}$

$\frak{\underline{\underline{\dag By\ substituting\ the\ value\ of\ "y"\ in\ equation(1):-}}}$

$\bf : \implies {x\ =\ 11\ -\ y} \\ \\ \bf : \implies {x\ =\ 11\ -\ 3} \\ \\ \bf : \implies {\underline{x\ =\ 8.}}$

Hence:-

$\sf \therefore {\underline{x\ =\ 8\ and\ y\ =\ 3.}}$