Question

Determine whether the system has no solution, one solution, or infinitely many solutions. If the system has one solution, name it.

–x+y= –5

3x+5y=15

Answer 1

(5, 0)

Explanation:

The slope of the first line is -(-1 / 1) = 1.

The slope of the second line is -(3 / 5) = -3/5.

Since the lines have different slopes, they intersect at a single point. Therefore, there is only one solution. To find it, solve the system of equations.

Using elimination, multiply the first equation by 3 and add it to the second.

-3x + 3y = -15

3x + 5y = 15

-------------------

8y = 0

y = 0

Using substitution, find x:

-x + 0 = -5

x = 5

The solution is (5, 0).