Question 579132
(1) {{{ 5x - 3y = 8 }}} 
(2) {{{ -5x + y = 4 }}}
To do substitution, take one of the equations
and isolate either {{{x}}} or {{{y}}} on one side
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Add {{{ 5x }}} to both sides of (2)
(2) {{{ y = 5x + 4 }}}
Now substitute this value of {{{y}}} for 
the {{{y}}} in equation (1)
(1) {{{ 5x - 3*(5x + 4 ) = 8 }}}
(1) {{{ 5x - 15x - 12 = 8 }}}
Add {{{12}}} to both sides
(1) {{{ -10x = 12 + 8 }}}
(1) {{{ -10x = 20 }}}
Divide both sides by {{{-10}}}
(1) {{{ x = -2 }}}
Now substitute this value for {{{x}}} back 
into either (1) or (2)
(1) {{{ 5*(-2) - 3y = 8 }}} 
(1) {{{ -10 - 3y = 8 }}}
Add {{{10}}} to both sides
(1) {{{ -3y = 18 }}}
Divide both sides by {{{-3}}}
(1) {{{ y = -6 }}}
check answers:
(2) {{{ -5x + y = 4 }}}
(2) {{{ -5*(-2) + (-6) = 4 }}}
(2) {{{ 10 - 6 = 4 }}}
(2) {{{ 4 = 4 }}}
and
(1) {{{ 5x - 3y = 8 }}} 
(1) {{{ 5*(-2) - 3*(-6) = 8 }}} 
(1) {{{ -10 + 18 = 8 }}}
(1) {{{ 8 = 8 }}}
OK