Y=5x+2 and 3x=-y+10 what is the soluion of equation

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Solve the following system:

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

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

Express the system in standard form:

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

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

Add 3/5 * (equation 1) to equation 2:

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

{0 x + (8 y) / 5 = 56/5 | (equation 2)

Multiply equation 2 by 5/8:

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

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

Subtract equation 2 from equation 1:

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

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

Divide equation 1 by - 5:

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

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

Collect results:

Answer: {x = 1 {y = 7