# 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

#### Explanation:

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 (**ONE** solution.

Hope that helped