Which equation can compare with 3x plus 4y equals eight to create a consistent and independent system

A consistent and independent system is any equation that only has one solution. So an another equation that can compare with this to create one solution is an equation that is perpendicular. The slope will be opposite and reciprocal.

This is the first equation in standard form: 3x + 4y = 8

Point-slope form is: y = -3/4x + 2

The second equation in standard form: y = 4/3x + 2

Point-slope form is: -4x + 3y = 6

As you can see, the slopes are opposite and reciprocal, which creates two perpendicular lines when graphed. You can graph these two lines, and see that they have one solution.

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