Mathematics
Easy

Question

# Solve the system:Y = -x + 10x + y = 5

## 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 = -x + 10 and x + y = 5So we can write,x + y =10       -------( 1)x + y = 5        --------(2)Now , we have a1/a2 a1/a2 = 1/1 =1and b1/b2 ,b1/b2 = 1/1 = 1and c1/c2c1/c2 = 10/5 = 2so here,1 = 1 ≠ 2 a1/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 = -x + 10 …(i)x + y = 5 …(ii)Substituting y from (i) in (ii), we get x + (-x + 10) = 510 = 5The statement 10 = 5 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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