Question

Systems of linear equations question 7 which system of equation has no solution

Answer 1

Answer:

The graph to the left and down corresponds to a system with no solution

Step-by-step explanation:

System of Equations

To solve a system of equations graphically, we must plot all the equations in one single graph. If the system has at least one solution, then both graphs must intersect, i.e., there must be at least one point in common. If no such point is found, then the system has no solution

LEt's take a look at the first graph. Both lines come from the origin, where they meet, so the point (0,0) is the solution of that system

The second graph has only one equation, with no blue line. It corresponds to a single equation, not to a system. Therefore we cannot evaluate if there is a solution

The third graph shows two parallel lines which we never expect to intersect. Since we need an intersection to find solutions, this graph is the one that corresponds to a system with no solution

Finally, the fourth graph has a common point, thus there is one solution to the system

Answer 2

Answer:

The bottom left system of equations has no solutions.

Step-by-step explanation:

A solution to the system of equations is a point where the graphs of equations  intersect, because the intersection point represents a point that is common to both equations; Therefore, a system that has no solutions, will have graphs that will never intersect.

Now, looking at the 4 graphs given, we see that the upper-left graph represents lines which intersect; therefore, this system has a solution.

The upper-right graph represents only one equation and not a system—it could well be that the red line hides another line that is exactly beneath it, in which case the system would have infinitely many solutions.

The bottom-left graph represents lines that are parallel—they are never going to meet; therefore, this system has no solutions.

The bottom-right graph represents lines that have a point of intersect, and therefore, have a solution.

Thus only the bottom-right graph has no solutions.