Maths-
General
Easy
Question
2x + 3y = 5
4x + cy = 8
In the system of equations above, c is a constant. For what value of c will there be no solution (x, y) to the system of equations?
- 3
- 4
- 5
- 6
The correct answer is: 6
HINT: There will be no solution for 2 systems of equations if the graphs of these 2 are parallel.
Complete step by step solution:
Let 2x + 3y = 5…(i) and 4x + cy = 8…(ii)
We know that line of equation is of the form y = mx + b
From this, we get line of equation of (i) as 
…(iii)
Line of equation of (ii) becomes 
…(iv)
It is given that there will be no solution to the system of equations.
We know that there will be no solution for the system of equations if the graphs of these lines are parallel.
Also, we know that if 2 equations have the same slope and different y intercepts, then the lines will be parallel.
From (iii) and (iv), we get that y intercepts are different but they will have the same slope.
That is, 
. On simplification, we get c = 6.
Hence when the value of c = 6 there will be no solution for the given system of equations.
Hence option D is the correct answer.
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