Mathematics
Easy

Question

# Solve the system:y = -x + 10x + y = 10

## 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 + 10 and x + y = 10.So , y = -x + 10    --(1)x + y = 10      --(2)We have a1 = 1 , b1 = 1 and c1 = 10And a2 = 1 , b2 = 1 and c2 = 10,Now , a1/a2 = 1, b1/b2 = 1and c1/ c2 = 10/10 = 1Therefore, a1/a2 = b1/b2 = c1/c2 Therefore , it solution having infinitely many solution.The correct answer is Infinitely many solution.Or, another way to solvey = -x + 10 …(i)x + y = 10 …(ii)Substituting y from (i) in (ii), we get x + (-x + 10) = 1010 = 10The statement 10 = 10 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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