Question

How many solutions does each system have?

System I:
x=y-3
2x - 2y = -6
System II:
5x + 2y = -7
15x + 6y = 21

Answers

O Both systems have no solution.
O System I has no solution and System II has an infinite number of solutions.
O System I has an infinite number of solutions and System II has no solution.
O Both systems have an infinite number of solutions.

Answer 1

System 1 has an infinite number of solutions and System 11 has no solution.

Explanation:

System 1:

x = y - 3

x - y = -3

2x - 2y = -6

Divide above by 2:

x - y = -3

So the 2 equations are identical

and they have an infinite number of solutions.

System 11:

5x + 2y = -7

15x + 6y = 21

Divide the above by 3:

5x + 2y = 7

Comparing this to the first equation the left sides are the same but right sides are different ( -7 and 7)/

There is no solution to this system.