2y = x + 3

5y = x - 7

What is the solution set of the given system?

{ (-1/3, - 4/3) }

{ (1/3, 4/3) }

{ (-29/3, - 10/3) }

{ (29/3, 10/3

{ (-29/3, - 10/3) }

Step-by-step explanation:

Solve the following system:

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

{5 y = x - 7 | (equation 2)

Express the system in standard form:

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

{-x + 5 y = - 7 | (equation 2)

Subtract equation 1 from equation 2:

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

{0 x+3 y = - 10 | (equation 2)

Divide equation 2 by 3:

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

0 x+y = (-10) / 3 | (equation 2)

Subtract 2 * (equation 2) from equation 1:

{-x+0 y = 29/3 | (equation 1)

{0 x+y = - 10/3 | (equation 2)

Multiply equation 1 by - 1:

{x+0 y = (-29) / 3 | (equation 1)

{0 x+y = - 10/3 | (equation 2)

Collect results:

Answer: {x = - 29/3, y = - 10/3