Question

The solution of the equation \[2x - 3y = 7\] and \[4x - 6y = 20\] is
A.\[x = 20,y = 12\]
B.\[x = 0,y = 0\]
C.No solution
D.\[x = 8,y = 5\]

Answer 1

Hint: Solution of an equation is nothing but that set of values of variables will satisfy the given set of equations. Thus we can either solve the equations for the value of x and y by traditional method or can check the values in option one by one.

Complete step-by-step answer:
Given the equations are, \[2x - 3y = 7\]→I and \[4x - 6y = 20\]→II
Now in equation II divide both sides by 2 we get,
\[2x - 3y = 10\]→III
\[2x - 3y = 7\]→I
But equation I and III has L.H.S. same but R.H.S. different. That is impossible for the same values of x and y. Thus it clearly indicates that a given set of equations has no solution.
So option C is the correct option.

Note: Here we have not checked for any other values from option. Even not for option B because on R.H.S. of both the equations we have a constant and that is not equal to 0. And don’t go for any other options in this particular problem because that will consume our time .