Which statement about the following system is correct?y=−2x+52x+y=8a. The system is inconsistent because the two equations actually represent the same line.b. The system is consistent because it has a solution.c. The system is consistent because it has no solution.d. The system is inconsistent because it has no solution.

A system of linear equations is said to be consistent if it has either one solution or infinitely many solutions in graphical manner lines are either intersect each other or pair of line are coincide . A system of linear equations is said to be inconsistent if it has no solution in other lines are parallel. In Algebraic form , two equations

a₁x₁ + b₁y₁+ c₁z₁ = 0 and a₂x₂+ b₂x₂ + c₂z₂ = 0

are Consistent if

a₁/a₂ ≠ b₁/b₂ ( unique solution)

a₁/a₂= b₁/b₂ = c₁/c₂ ( infinite solutions)

Inconsistent if

a₁/a₂ = b₁/b₂ ≠ c₁/c₂ ( No solution)

We have given a linear system of equations,

y + 2x = 5 ---(1)

2x + y = 8 ---(2)

Here, two equations consists two variables x and y. Comparing equation (1) and (2) with standard above equations, we get a₁= 2 , b₁ = 1 , C₁ = -5 , a₂= 2 , b₂= 1 , c₂ = -8 , we see here that a₁/a₂= 2/2= 1 = b₁/b₂=1 ≠ c₁/c₂ = 5/8

Hence, the given system of equations is inconsistent and no solution exist.

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