How many solutions does the following system have?

Question

2x+3y=1
-3x-2y=-1

Answer 1

To find the number of solutions for this system, we can use the method of solving simultaneous equations.

Multiplying the first equation by 2 and the second equation by 3, we get:

4x + 6y = 2
-9x - 6y = -3

Adding the two equations together, we get:

-5x = -1

Dividing by -5, we find:

x = 1/5

Substituting the value of x into either of the original equations, we get:

2(1/5) + 3y = 1
2/5 + 3y = 1
3y = 3/5
y = 1/5

Therefore, the system has a unique solution: x = 1/5, y = 1/5.