Question

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

Answer 1

The answers

C.) no solution

Answer 2

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.