Mathematics
Easy

Question

# Solve the system:y = x + 35y = 5x + 15

## No solution(11, 8)(5, 15)Infinitely many solutions Hint:

## The correct answer is: Infinitely many solutions

### Here we have to find the system of equation.Firstly, we have given equation y =x + 3 and 5y = 5x + 15.So , y = x + 3 --(1)5y = 5x + 15 --(2)We have a1 = 1 , b1 = 1 and c1 = 3 And a2 = 5 , b2 = 5 and c2 = 15,Now , a1/a2 = 1/5 , b1/b2 = 1/5and c1/ c2 = 3/15 = 1/5 therefore, a1/a2 = b1/b2 = c1/c2 Therefore , it solution having infinitely many solution.The correct answer is Infinitely many solution.Or simply,y = x + 3 …(i)5y = 5x + 15 …(ii)Substituting y from (i) in (ii), we get 5(x + 3) = 5x + 155x + 15 = 5x + 1515 = 15The statement 15 = 15 is an identity, so the system of equations has infinitely many solutions.

In this question, we have solve this question by system of equation we have , if (a1/a2) = (b1/b2) = (c1/c2) then it is infinitely many solutions, if  (a1/a2) = (b1/b2) ≠ (c1/c2) and if (a1/a2) ≠(b1/b2) then it is unique solution.

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