Solving systems of equations using any method

x = 5, y = 2

Step-by-step explanation:

Solve the following system:

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

{y = (3 x) / 5 - 1 | (equation 2)

Express the system in standard form:

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

{ - (3 x) / 5 + y = - 1 | (equation 2)

Subtract 3/7 * (equation 1) from equation 2:

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

{0 x + (4 y) / 7 = 8/7 | (equation 2)

Multiply equation 1 by 5:

{ - (7 x) + 5 y = - 25 | (equation 1)

{0 x + (4 y) / 7 = 8/7 | (equation 2)

Multiply equation 2 by 7/4:

{ - (7 x) + 5 y = - 25 | (equation 1)

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

Subtract 5 * (equation 2) from equation 1:

{ - (7 x) + 0 y = - 35 | (equation 1)

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

Divide equation 1 by - 7:

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

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

Collect results:

Answer: {x = 5, y = 2