Respuesta :
Answer:
He is correct.
Step-by-step explanation:
Because a linear system in three variables means that they have solutions if the all three have points in common in R3 space. But, in the case that they don't have any solution mean the opposite, they don't have points in common in R3 space.
In a linear system, variables must be related through common points. So, graphically, you should draw intersecting geometrical places in order to show the intersections, wich are the common results or points that are the solutions of the linear system.
A linear system of equation in three variables has no solution is the correct statement.
What is linear equation?
" Linear equation is defined as the equation whose variables with highest degree one."
According to the question,
Given statement,
A linear system of equation in three variables has no solution.
Verification:
Consider a example of linear system of equation with three variables
[tex]2x-4y +z=3 \ \ \ \ \ \ \ \ \ \ \ \ \ \ (1)[/tex]
[tex]8x-2y+ 4z=7 \ \ \ \ \ \ \ \ \ \ \ \ \ (2)[/tex]
[tex]-4x+y -2z=-14\ \ \ \ \ \ \ \ \ \ (3)[/tex]
Solve linear equation to get the solution
Multiply [tex](3)[/tex] by [tex]2[/tex] and add it to [tex](2)[/tex],
[tex]\ \ 8x-2y+ 4z=7\\\\-8x+2y-4z =-28[/tex]
we get,
[tex]0x+0y + 0z = -21[/tex] which is not possible and has no solution.
Hence, linear system of equation has no solution is the correct statement.
Learn more about linear equation here
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