Question

A system of linear equations in two variables is inconsistent, if their graphs

Answer 1

Answer:

If a consistent system has an infinite number of solutions, it is dependent . When you graph the equations, both equations represent the same line. If a system has no solution, it is said to be inconsistent . The graphs of the lines do not intersect, so the graphs are parallel and there is no solution.

Answer 2

Answer:

They do not intersect with each other.

Step-by-step explanation:

1. There is at least one solution to the equations in the consistent system. If a consistent system, like the one we just looked at, has a single solution, it is said to be an independent system.
2. The two lines cross at one location in the plane and have different slopes. If the equations' slopes and y-intercepts match, the system is said to be consistent and regarded as a dependent system.
3. In other words, the equations depict the same line because the lines are parallel. A coordinate pair that fulfils the system is represented by each point on the line. There are therefore countless possible answers.
4. An inconsistent system of linear equations, in which the equations represent two parallel lines, is another sort of linear equation system. Or in simple terms, If the lines of a system of two linear equations in two variables coincide, the system is dependent and consistent.
5. When there is at least one solution, a system of two linear equations is consistent. Only when there are infinitely many possible answers is it dependently consistent. If there is no solution, the two linear equations a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0 are inconsistent.
6. The parallel lines that make up the graphical depiction of an inconsistent system never cross. If the graphs of two linear equations in two variables do not meet anywhere, then the system is inconsistent.

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