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A consistent, independent system of equations is a system with __________.

a) intersecting lines that have different slopes and different y-intercepts
b) intersecting lines that have the same slope and the same y-intercept
c) intersecting lines that have the same slope but different y-intercepts
d) only one line

User Hypnotic
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Final answer:

A consistent, independent system of equations refers to intersecting lines with different slopes and different y-intercepts, indicating a single solution point where they meet.

Step-by-step explanation:

A consistent, independent system of equations is a system with intersecting lines that have different slopes and different y-intercepts. This means that each equation in the system represents a straight line, and because these lines intersect at a single point, there is exactly one set of values for the independent and dependent variables that satisfy both equations simultaneously.

In the context of linear equations of the form y = a + bx, where a is the y-intercept and b is the slope, two lines are considered independent if they have different slopes, meaning they are not parallel, and therefore will intersect at a point. The y-intercept a represents the point where the line crosses the y-axis, whereas the slope b indicates the rise over run of the line on the graph.

User Harish Dhami
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