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:

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

first one

step-by-step explanation:

step-by-step explanation:

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