Mathematics
Easy

Question

# Solve the system:y = -2x + 34x + 2y = 6

Hint:

## The correct answer is: Infinitely many solutions

### Here we have to find the system of equation.Firstly, we have given equation y = -2x + 3 and 4x + 2y = 6.So , y = -2x + 3      --(1)4x + 2y = 6     --(2)We have a1 = 2 , b1 = 1 and c1 = 3 And a2 = 4 , b2 = 2 and c2 = 6,Now ,a1/a2 = 2/4 = 1/2 ,b1/b2 = 1/2 and c1/ c2 = 3/6 = 1/2Therefore, a1/a2 = b1/b2 = c1/c2 Therefore , it solution having infinitely many solution.The correct answer is Infinitely many solution.Or, an another way to solve.y = -2x + 3 …(i)4x + 2y = 6 …(ii)Substituting y from (i) in (ii), we get 4x + 2(-2x + 3) = 64x – 4x + 6 = 66 = 6The statement 6 = 6 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.