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Q: Does the graph of a system of equations with different slopes have no solutions?

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No the only time that a system of equations would have no solutions is when the two equations have the same slope but different y-intercepts which would mean that they are parallel lines. However, if they have different slopes and different y-intercepts than the solution would be where the two lines 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.

The slopes (gradients) of the two equations are different.

If a system of equations is inconsistent, there are no solutions.

As there is no system of equations shown, there are zero solutions.

The system of equations can have zero solutions, one solution, two solutions, any finite number of solutions, or an infinite number of solutions. If it is a system of LINEAR equations, then the only possibilities are zero solutions, one solution, and an infinite number of solutions. With linear equations, think of each equation describing a straight line. The solution to the system of equations will be where these lines intersect (a point). If they do not intersect at all (or maybe two of the lines intersect, and the third one doesn't) then there is no solution. If the equations describe the same line, then there will be infinite solutions (every point on the line satisfies both equations). If the system of equations came from a real world problem (like solving for currents or voltages in different parts of a circuit) then there should be a solution, if the equations were chosen properly.

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.

A system of linear equations can only have: no solution, one solution, or infinitely many solutions.

Solve both equations for y, that is, write them in the form y = ax + b. "a" is the slope in this case. Since the two lines have different slopes, when you graph them they will intersect in exactly one point - therefore, there is one solution.

infinintly many. for apex.

False. There can either be zero, one, or infinite solutions to a system of two linear equations.

if a dependent system of equation is solved, how many solutions will there be?

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