Solve the following system:

{y = 2 x - 7 | (equation 1)

5 x - 2 y = 15 | (equation 2)

Express the system in standard form:

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

5 x - 2 y = 15 | (equation 2)

Swap equation 1 with equation 2:

{5 x - 2 y = 15 | (equation 1)

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

Add 2/5 × (equation 1) to equation 2:

{5 x - 2 y = 15 | (equation 1)

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

Multiply equation 2 by 5:

{5 x - 2 y = 15 | (equation 1)

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

Add 2 × (equation 2) to 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 and y = -5**

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May 17, 2017