How do you determine whether a linear system has one solution, many solutions, or no solution when given 3x-y= -4 and x+ 3y= -28?
1 Answer
This system has one solution.
Explanation:
A linear system may have either:
1 solution (lines cross at one point),
no solutions (lines are parallel),
or infinitely many solutions (lines are actually the same line).
The way to figure out which type of problem you are looking at is to compare the slopes. If the slopes are different you will definitely have 1 solution.
If the slopes are the same, you must see if they have the same y-intercept. If the y-intercepts are the same, then the 2 lines are the same, so you have infinitely many solutions.
In this system we can find the slope by solving for y and looking at the coefficient in front of x.
Different slopes, so only one solution.
