Question

A system of equations is shown:

2x = -y + 6
--4x + 3y = 8
What is the solution to this system of equations?
0 (-1,-4)
O (1.4)
(4, 1)
(-4,-1)

Answer 1

`\large\underline{\bf \red{Step \:by\: Step \:Explanation:}}`

Given two equations are :

• 2x = - y + 6.
• -4 x + 3y = 8 .

We may write them as ,

• 2x + y - 6 = 0 .................(i)
• 4x - 3y + 8 = 0 ...............(ii)

Multiplying equⁿ (i) by 2 :

⇒ 2(2x + y - 6 ) = 0.

⇒ 4x + 2y - 12 = 0 .....................(iii) .

Subtract equⁿ (ii) from equⁿ (iii) :-

⇒ 4x + 2y - 12 = 0

ㅤ- 4x + 3y - 8 = 0 [ Sign changes ]

__________________

⇒ 5y - 20 = 0.ㅤㅤㅤㅤㅤ

⇒ 5y = 20.

⇒ y = 20/5.

⇒ y = 4

Put this value in (i) to obtain x .

⇒ 2x + y - 6 = 0.

⇒ 2x +4 - 6 = 0.

⇒ 2x - 2 = 0.

⇒2x = 2 .

⇒ x = 2/2.

⇒ x = 1 .

Hence the value of x is 1 & y is 4.

`\boxed{\purple{\bf\pink{\dag}\:Hence\:the\: correct\: option\:is\:[b]\:(1,4)}}`