Find the value of y for the following system of equations 5x + 3y = 10 x = y - 6

x = - 1, y = 5

Step-by-step explanation:

Solve the following system:

{5 x + 3 y = 10 | (equation 1)

x = y - 6 | (equation 2)

Express the system in standard form:

{5 x + 3 y = 10 | (equation 1)

x - y = - 6 | (equation 2)

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

{5 x + 3 y = 10 | (equation 1)

0 x - (8 y) / 5 = - 8 | (equation 2)

Multiply equation 2 by - 5/8:

{5 x + 3 y = 10 | (equation 1)

0 x+y = 5 | (equation 2)

Subtract 3 * (equation 2) from equation 1:

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

0 x+y = 5 | (equation 2)

Divide equation 1 by 5:

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

0 x+y = 5 | (equation 2)

Collect results:

Answer: {x = - 1, y = 5