Question

y = 5x – 1
–15x – 3y = 3
How many solutions does this linear system have?

one solution: (0, –1)
one solution: (1, 4)
no solution
infinite number of solutions

Answer 1

Substitute y = 5x − 1 into the second equation:
-15x − 3(5x − 1) = 3
-15x − 15x + 3 = 3
-30x = 0 → x = 0
Then y = 5(0) − 1 = −1.

So there is one solution: (0, −1).