How do you determine whether a linear system has one solution, many solutions, or no solution when given x + 6y = 28 and 2x - 3y = -19?
1 Answer
Rearrange the two equations into slope intercept format and compare the slopes. Since the slopes are different we have a pair of intersecting lines, that is exactly one solution.
Explanation:
Given
y = -1/6 x + 14/3
Given
y = 2/3 x + 19/3
Both of these equations are now in slope intercept form, so we can see that the slopes of the two lines represented by the equations are different, the first being
So the two lines are not parallel and they intersect at exactly one point. That is the two equations can be satisfied simultaneously for exactly one pair of
graph{(x+6y-28)(2x-3y+19) = 0 [-10.625, 9.375, -2.2, 7.8]}
