Question

# −6x+8y=2 ,   3x−4y=−3 Consider the system of equations above. How many (x,y) solutions does this system have?Exactly one solutionNo solutionsExactly two solutionsInfinitely many solutions

Solution

## The correct option is B No solutionsLets see   −6x+8y=2 3x−4y=−3 Ratio of x coefficient  =−63=−2 Ratio of y coefficient =8−4=−2 Ratio of constant =2−3 So from here, we can see that  ratio of x coefficient = Ratio of y coefficient ≠ Ratio of constant Therefore, these two lines are paralled and there is no solution of the given system of equations.

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