Question

The solution of the equations x+y=5, 2x-3y=5 is *
1 point
X=4,y=1
X=1, y=4
X=-4,y=1
X=-1,y=4​

Answer 1

Answer :

x = 4

y = 1

Given :

x + y = 5

⇒ x = 5 - y ..........(1)

and

2x - 3y = 5 .......(2)

To Find :

The value of x and y

Solution :

Putting the value of x from (1) in (2)

⇒ 2(5 - y) - 3y = 5

⇒ 10 - 2y - 3y = 5

⇒ -5y = 5 - 10

⇒ -5y = -5

⇒ y = 1

Now putting the value of y in (1)

x = 5 - 1

⇒ x = 4

Verification :

Using the values in one of the equation given in the question we have :

x + y = 5

⇒ 4 + 1 = 5

⇒ 5 = 5

Answer 2

Answer:

• x + y = 5⠀⠀⠀⠀⠀⠀⠀— eq. ( I )
• 2x – 3y = 5⠀⠀⠀⠀⠀ — eq. ( II )

$\underline{\bigstar\:\textsf{Multiplying eq. ( I ) by 3 \& Adding :}}$

$\dashrightarrow\sf\:\:3x+3y=15\\\\\dashrightarrow\sf\:\:2x-3y=5\\\dfrac{\qquad\qquad\qquad\qquad\qquad}{}\\\dashrightarrow\sf\:\:3x+2x=15+5\\\\\\\dashrightarrow\sf\:\:5x=20\\\\\\\dashrightarrow\sf\:\:x=\dfrac{20}{5}\\\\\\\dashrightarrow\:\:\underline{\boxed{\sf x=4}}$

$\rule{150}{1}$

$\underline{\bigstar\:\textsf{Putting value of x in eq. ( I ) :}}$

$\dashrightarrow\sf\:\:x+y=5\\\\\\\dashrightarrow\sf\:\:4+y=5\\\\\\\dashrightarrow\sf\:\:y=5-4\\\\\\\dashrightarrow\:\:\underline{\boxed{\sf y=1}}$

⠀

$\therefore\:\underline{\textsf{Solution of Equation is A) \textbf{x = 4 \& y = 1}}}.$