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Q: How do you know if a system has one solution?

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Two or more straight lines meeting at one point.

No It;s Not A Solution > :)

visual,intuitive

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.

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Related questions

Provide a system of equations in slope-intercept form that has one solution. Using complete sentences, explain why this system has one solution.

An independent system has one solution.

Independent system.

If one part of the solution is soluble, then it is an aqueous 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.

They will be a set of lines meeting at one point - the solution.

one solution

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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.

If the lines intersect, then the intersection point is the solution of the system. If the lines coincide, then there are infinite number of the solutions for the system. If the lines are parallel, there is no solution for the system.

a linear equation

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