Question

# Given that $$kx - 3y = 4$$and $$4x - 5y = 7$$In the system of equations above, $$k$$ is a constant and $$x$$ and $$y$$ are variables. For what value of $$k$$ will the system of equations have no solution?

A
125
B
167
C
167
D
125

Solution

## The correct option is A $$\dfrac {12}{5}$$Let $$kx - 3y = 4$$ ..(1)and $$4x - 5y = 7$$ ..(2)Multiplying equation (1) by $$5$$ and equation (2) by $$3$$, we have$$5kx - 15y = 20$$ ..(3)$$12x - 15y = 21$$ ..(4)Since the coefficient of $$y$$ is same in equations (3) and (4), and the terms on right hand side of equality are different, the coefficients of $$x$$ cannot be the same.$$\therefore 5k \neq 12$$$$\therefore k \neq \cfrac{12}{5}$$Maths

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