How many solutions does the following system have?

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

x = 1/5, y = 1/5

Step-by-step explanation:

Solve the following system:

{2 x + 3 y = 1 | (equation 1)

-3 x - 2 y = - 1 | (equation 2)

Swap equation 1 with equation 2:

{ - (3 x) - 2 y = - 1 | (equation 1)

2 x + 3 y = 1 | (equation 2)

Add 2/3 * (equation 1) to equation 2:

{ - (3 x) - 2 y = - 1 | (equation 1)

0 x + (5 y) / 3 = 1/3 | (equation 2)

Multiply equation 1 by - 1:

{3 x + 2 y = 1 | (equation 1)

0 x + (5 y) / 3 = 1/3 | (equation 2)

Multiply equation 2 by 3:

{3 x + 2 y = 1 | (equation 1)

0 x+5 y = 1 | (equation 2)

Divide equation 2 by 5:

{3 x + 2 y = 1 | (equation 1)

0 x+y = 1/5 | (equation 2)

Subtract 2 * (equation 2) from equation 1:

{3 x+0 y = 3/5 | (equation 1)

0 x+y = 1/5 | (equation 2)

Divide equation 1 by 3:

{x+0 y = 1/5 | (equation 1)

0 x+y = 1/5 | (equation 2)

Collect results:

Answer: {x = 1/5, y = 1/5