5x - 7y = 58

y = - x - 2

X=

Y=

x = 11/3, y = - 17/3

Step-by-step explanation:

Solve the following system:

{5 x - 7 y = 58 | (equation 1)

y = - x - 2 | (equation 2)

Express the system in standard form:

{5 x - 7 y = 58 | (equation 1)

x + y = - 2 | (equation 2)

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

{5 x - 7 y = 58 | (equation 1)

0 x + (12 y) / 5 = (-68) / 5 | (equation 2)

Multiply equation 2 by 5/4:

{5 x - 7 y = 58 | (equation 1)

0 x+3 y = - 17 | (equation 2)

Divide equation 2 by 3:

{5 x - 7 y = 58 | (equation 1)

0 x+y = (-17) / 3 | (equation 2)

Add 7 * (equation 2) to equation 1:

{5 x+0 y = 55/3 | (equation 1)

0 x+y = - 17/3 | (equation 2)

Divide equation 1 by 5:

{x+0 y = 11/3 | (equation 1)

0 x+y = - 17/3 | (equation 2)

Collect results:

Answer: {x = 11/3, y = - 17/3