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)
Answers
[tex]\large\underline{\bf \red{Step \:by\: Step \:Explanation:}}[/tex]
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.
[tex]\boxed{\purple{\bf\pink{\dag}\:Hence\:the\: correct\: option\:is\:[b]\:(1,4)}}[/tex]
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