Mathematics
Easy

Question

# Solve the system:y = 2x + 83y = 6x + 24

## 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 = 2x + 8 and 3y = 6x + 24.So , y = 2x + 8          --(1)3y = 6x + 24      --(2)We have a1 = 2 , b1 = 1 and c1 = 8And a2 = 6 , b2 = 3 and c2 = 24,Now , a1/a2 = 1/3 , b1/b2 = 1/3and c1/ c2 = 8/24 = 1/3therefore, a1/a2 = b1/b2 = c1/c2 Therefore , it solution having infinitely many solution.The correct answer is Infinitely many solution.Or,y = 2x + 8 …(i)3y = 6x + 24 …(ii)Substituting y from (i) in (ii), we get 3(2x + 8) = 6x + 246x + 24 = 6x + 2424 = 24The statement 24 = 24 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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