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No it is not impossible, as long as only one of the lines is horizontal. Since you are referring to lines, it sounds like a 2-variable system (with x and y, for example). An example would be something like [in a word problem]: find two numbers, whose sum is 12; and one of the numbers is 5. So the numerical system could look something like:

x + y = 12 and y = 5. The y = 5 is a horizontal line. To solve, just plug y=5 into the first equation, and solve for x=7, so the point of intersection is (7,5). As long as the two lines are not parallel, there will be a solution.

Q: Is it impossible for a system of equations in which one of the lines is a horizontal line to have a solution?

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there is no linear equations that has no solution every problem has a solution

A system of equations may have any amount of solutions. If the equations are linear, the system will have either no solution, one solution, or an infinite number of solutions. If the equations are linear AND there are as many equations as variables, AND they are independent, the system will have exactly one solution.

The solution is the coordinates of the point where the graphs of the equations intersect.

Not necessarily.

its a system of equations, with no solution

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there is no linear equations that has no solution every problem has a solution

A system of equations with exactly one solution intersects at a singular point, and none of the equations in the system (if lines) are parallel.

A system of equations may have any amount of solutions. If the equations are linear, the system will have either no solution, one solution, or an infinite number of solutions. If the equations are linear AND there are as many equations as variables, AND they are independent, the system will have exactly one solution.

The solution of a system of linear equations is a pair of values that make both of the equations true.

A system of equations will have no solutions if the line they represent are parallel. Remember that the solution of a system of equations is physically represented by the intersection point of the two lines. If the lines don't intersect (parallel) then there can be no solution.

Graph both equations on the same graph. Where they intersect is the solution to the system of equations

No because there are no equations there to choose from.

The solution is the coordinates of the point where the graphs of the equations intersect.

If the equations or inequalities have the same slope, they have no solution or infinite solutions. If the equations/inequalities have different slopes, the system has only one solution.

visual,intuitive

Inconsistent.

its a system of equations, with no solution