How do you determine whether a linear system has one solution, many solutions, or no solution when given 7x+4y=26 and 3x-8y=-18?

1 Answer
Oct 21, 2015

Find the slope and y-intercept of each linear system


1) If the slopes are different, then there is ONE solution.

2) If the slopes are the same, but different y-intercepts, then there are NO solutions.

3) Finally, if the slopes and y-intercepts are both the same, then there are an INFINITE number of solutions.

In your example, the two systems have different slopes (#-7/4 ne 3/8#), so there is only ONE solution.

Hope that helped