How do you determine whether a linear system has one solution, many solutions, or no solution when given 3x - y = -2 and -4x + 2y= 5?
1 Answer
Two lines with different slopes will always intersect at exactly one point (i.e. they will have exactly one solution).
Explanation:
This system of lines has one solution.
Bonus 1: Slope Determination
Given a linear equation in standard form
its slope is
Bonus 2: Determining the Solution for the Given System
[1]
[2]
Multiply [1] by
[3]
Add [2] and [3]
[4]
Divide both sides by
[5]
Substitute
[6]
Simplify
[7]
Divide by
[8]
Bonus 3: For Those Who Like To Be Picky
The rule stated in the "Answer" assumes the two lines lie in a common plane. Two lines (in 3 dimensional space, for example) may not intersect even with different slopes.