How many solutions does the following system have?

Question

2x+3y=1
-3x-2y=-1
A. Infinitely many solutions
B. two solutions
C. one solution
D. no solutions

Answer 1

To solve this system, we can multiply the first equation by 2 and the second equation by 3 in order to eliminate x.

Multiplying the first equation by 2 gives:
4x + 6y = 2.

Multiplying the second equation by 3 gives:
-9x - 6y = -3.

Adding the two new equations together eliminates y:
4x - 9x + 6y - 6y = 2 - 3.
-5x = -1.

Dividing both sides of the equation by -5 gives:
x = 1/5.

Substituting this value for x in the first equation:
2(1/5) + 3y = 1.
2/5 + 3y = 1.
Subtracting 2/5 from both sides of the equation gives:
3y = 1 - 2/5.
3y = 5/5 - 2/5.
3y = 3/5.
Dividing both sides of the equation by 3 gives:
y = 1/5.

So, the system has only one solution, which is x = 1/5 and y = 1/5.

Therefore, the correct answer is C. one solution.