Mathematics
Easy

Question

# Solve the system:y = 2x + 83y = 6x + 30

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

## The correct answer is: No solution

### Here we have solve the system of equation and find x and y.Firstly , we are given, y = 2x + 8 and 3y = 6x + 30So we can write,2x – y = -8       -------( 1)6x – 3y = -30    -------(2)Now , we have a1/a2 a1/a2 = 2/6 =1/3and b1/b2 ,b1/b2 = -1/-3 = 1/3and c1/c2c1/c2 = -8/-30= 4/15so here,1/3 = 1/3 ≠ 4/15a1/a2 = b1/b2 ≠ c1/c2Therefore the system of equation of no solution.The correct answer is No solution.Or, another way to solve question..y = 2x + 8 …(i)3y = 6x + 30 …(ii)Substituting y from (i) in (ii), we get 3(2x + 8) = 6x + 306x + 25 = 6x + 3025 = 30The statement 25 = 30  is false, so the system of equations has no solution.

In this question, we have to find the system of equation. 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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