Question 154388
Collecting like terms is the correct first step
{{{(2x+y) + (3-5x)i = 1 -7i}}}
{{{(2x + y -1) + (3+7 -5x)i = 0}}}
{{{(2x+ y -1) + (10-5x)i = 0}}}

For a complex number equal zero, both the real and the imaginary parts must be 0.
So
{{{2x + y -1 = 0}}}
{{{10-5x = 0}}}
{{{-5x = -10}}}
{{{x = 2}}}

Substituting back into the real part
{{{2x + y -1 = 0}}}
{{{4 + y - 1 = 0}}}
{{{y = -3}}}


Make sense now?