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Systems of equations with different slopes and different y-intercepts have one solution. Is this statement:

a) Always true
b) Sometimes true
c) Never true

1 Answer

1 vote

Final answer:

Systems of equations with different slopes and different y-intercepts always intersect in exactly one point, provided that we are discussing lines in a two-dimensional plane.

Step-by-step explanation:

The statement "Systems of equations with different slopes and different y-intercepts have one solution" is always true. In linear algebra, a system of equations composed of straight lines will intersect exactly once if the lines have different slopes. Since slope determines the steepness and direction of a line, and the y-intercept determines where the line crosses the y-axis, different values for these parameters guarantee that the lines are not parallel and therefore will intersect at a single point. This is because lines with different slopes are not parallel and must cross at some point, creating one solution for the system.

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