What is the solution of this system of linear equations? 3y=3/2x+6 1/2y-1/4x=3 A. (3,6) B. (2,1) C. No solution D. Infinite number of solutions

Question

asked Apr 15, 2018 38.3k views

2 Answers

Fahu · Answer 1 · 2018-04-22T01:22:51+0000

Answer: The correct option is (C) No solution.

Step-by-step explanation: We are given to find the solution of the following system of equations :

$3y=(3)/(2)x+6~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\\\(1)/(2)y-(1)/(4)x=3~~~~~~~~~~~~~~~~~~~~~~~~~(ii)$

Dividing equation (i) by 3 on both sides, we get

$(3y)/(3)=(3)/(3*2)x+(6)/(3)\\\\\\\Rightarrow y=(1)/(2)x+2~~~~~~~~~~~~~~~~~~~~~(iii)$

Substituting the value of y from equation (iii) in equation (ii),we get

$(1)/(2)y-(1)/(4)x=3\\\\\\\Rightarrow (1)/(2)\left((1)/(2)x+2\right)-(1)/(4)x=3\\\\\\\Rightarrow (1)/(4)x+1-(1)/(4)x=3\\\\\Rightarrow 1=3,$

which CANNOT be true.

So, the given system of equations will have no solution.

Option (C) is CORRECT.