Question

2. Solve: (1) 4x - 3y =6; x + 3y = 9
(ii) 3x +2y = 14 ; x - 4y =-7​

Answer 1

(i)

Given:

Two equations in two variables:

• 4x-3y=6----------------(1)
• x+3y=9-----------------(2)

To Find:

Value of x and y

Solution:

On adding (1) and (2), we get

$\sf{4x-3y=6}\\\sf{\:\:x+3y=9}\\\rule{59}{0.5}\\\sf{\:\:5x+\:\:0=15}$

$\rightarrow\sf{5x=15}$

$\rightarrow\sf{x=\dfrac{\cancel{15}}{\cancel{5}}}$

$\rightarrow\sf{x=3}$

On putting value of x in (1), we get

➳ 4(3)-3y=6

➳ 12-3y=6

➳ -3y=6-12

➳ -3y=-6

➳ y=2

Hence, the value of x=3 and y=2.

$\rule{180}{2}$

(ii)

Given:

Two equations in two variables:

• 3x+2y=14---------------(1)
• x-4y= -7-----------------(2)

To Find:

Value of x and y

Solution:

On multiplying (1) by 2, we get

6x+4y=28---------------(3)

On adding (2) and (3), we get

$\sf{\:\:\:x-4y=-7}\\\sf{\:6x+4y=28}\\\rule{61}{0.5}\\\sf{\:7x+\:\:0=21}$

$\rightarrow\sf{7x=21}$

$\rightarrow\sf{x=\dfrac{\cancel{21}}{\cancel{7}}}$

$\rightarrow\sf{x=3}$

On putting value of x in (2), we get

➳ 3-4y= -7

➳ -4y= -7-3

➳ -4y= -10

$\rightarrow\sf{y=\dfrac{\cancel{-10}}{\cancel{-4}}}$

$\rightarrow\sf{y=\dfrac{5}{2}}$

Hence, the value of x=3 and y=5/2.