EduGoog

The equations 4x + 7y - 10 =0 and 20x + 35y - 50 = 0 are :

Option:
A. consistent and have a unique solution.
B. consistent and have infinitely many solutions.
C. inconsistent.
D. None of these
Answer: B . consistent and have infinitely many solutions.

Justification:

Equation I:-  4x + 7y = 10
Equation II:- 20x + 35y = 50

.`. Multiply Equation I by 5.
(4x + 7y = 10) x (5) = (20x + 35y = 50)
We get Equation III = 20x + 35y = 50
Now, Subtract Equation III with Equation II.
(20x + 35y = 50) - (20x + 35y = 50)
.`. (20x - 20x) + (35y - 35y) = (50 - 50)
.`. (0) + (0) = (0)

So, the given equations, have an infinite number of solutions and hence they are consistant also.



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