How do you determine whether a linear system has one solution, many solutions, or no solution when given x+ 5y=1 and -3x +4y= 16?

1 Answer
George C.
Oct 25, 2015

Rearrange in slope intercept form and notice that the slopes are different, so these equations represent two non-parallel lines that intersect at one point - that is one solution.

Explanation:

Given x+5y=1, subtract x from both sides, then divide both sides by 5 to get:

y = -1/5 x + 1/5

Given -3x+4y=16, add 3x to both sides, then divide both sides by 4 to get:

y = 3/4 x + 4

So these equations represent lines with slope -1/5 and 3/4.

Since the slopes are different, the lines will intersect at exactly one point.

graph{(x+5y-1)(-3x+4y-16) = 0 [-10, 10, -4.5, 5.5]}

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