The system of equations in graph B will have no solution. The correct option is A, Graph B.
What is a system of equations?
Inconsistent System
For a system of equations to have no real solution, the lines of the equations must be parallel to each other.
Consistent System
1. Dependent Consistent System
For a system of the equation to be a Dependent Consistent System, the system must have multiple solutions for which the lines of the equation must be coinciding.
2. Independent Consistent System
For a system of the equation to be an Independent Consistent System, the system must have one unique solution for which the lines of the equation must intersect at a particular.
A system of the equation has no solution when the line of the equations does not intersect each other at any point on the graph. Since two parallel lines never intersect each other, therefore, it can be concluded that a graph that has two parallel lines is a kind of system of equations that will have no solution.
For the given case since there is only one graph in which the two lines are parallel that is Graph B.
Hence, the system of equations in graph B will have no solution.
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