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The graph of a system of equations with the same slope will have no solution, unless they have the same y intercept, which would give them infinitely many solutions. Different slopes means that there is one solution.

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โˆ™ 2011-02-13 09:37:30
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A polynomial of degree zero is a constant term

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Q: Does the graph of a system of equations with different slopes have no solutions?
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Systems of equations with different slopes and different y-intercepts have no solutions?

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.

How do you know if a system has one solution?

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.

A system of two linear equations has exactly one solution if?

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

If a system of equations is inconsitient how many solutions will it have?

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

How many solutions does the system of linear equations shown have?

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

What are the possible solutions for a system of equations?

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.

If a system of equations is independent how many soultions will it have?

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.

Why a system of linear equations cannot have exactly two solutions?

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

Does this system of equations have one solution no solutions or an infinite number of solutions 2x - y equals 8 and x plus y equals 1?

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.

Imagine that you are given two linear equations in slope-intercept form. You notice that the slopes are different but the y-intercepts are the same. How many solutions would you expect for this system?

infinintly many. for apex.

There is a system of linear equations with exactly two solutions is it true or false?

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

If a dependent system of equations is solved how many solutions will there be?

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

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