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
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
#y = -1/5 x + 1/5#
Given
#y = 3/4 x + 4#
So these equations represent lines with slope
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]}