Solve the system of equations given

5x+2y=9

2x-3y=15

A. (3,-3)

B. (-3,12)

C. (12,-3)

D. (-3,3)

{x = 3, y = - 3 thus the answer is A

Step-by-step explanation:

Solve the following system:

{5 x + 2 y = 9 | (equation 1)

{2 x - 3 y = 15 | (equation 2)

Subtract 2/5 * (equation 1) from equation 2:

{5 x + 2 y = 9 | (equation 1)

{0 x - (19 y) / 5 = 57/5 | (equation 2)

Multiply equation 2 by 5/19:

{5 x + 2 y = 9 | (equation 1)

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

Multiply equation 2 by - 1:

{5 x + 2 y = 9 | (equation 1)

{0 x+y = - 3 | (equation 2)

Subtract 2 * (equation 2) from equation 1:

{5 x+0 y = 15 | (equation 1)

{0 x+y = - 3 | (equation 2)

Divide equation 1 by 5:

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

{0 x+y = - 3 | (equation 2)

Collect results:

Answer: {x = 3, y = - 3

A) 5x+2y=9

B) 2x-3y=15

Multiply A) by 1.5

A) 7.5x + 3y = 13.5 then add it to B)

B) 2x-3y=15

9.5x = 28.5

x = 3

5*3 + 2y=9

2y = - 6

y = - 3

answer is A