Question 574330
(1) {{{ 5x+2y=-11 }}}
(2) {{{ 7x-3y=19 }}}
Multiply (1) by {{{3}}}
Multiply (2) by {{{2}}}
Then add the equations
(1) {{{ 15x+6y=-33 }}}
(2) {{{ 14x-6y=38 }}}
{{{ 29x = 5 }}}
{{{ x = 5/29 }}}
Plug this back into either (1) or (2)
(2) {{{ 7*(5/29) - 3y=19 }}}
Now multiply both sides by {{{ 29 }}}
( I'll go slowly )
(2) {{{ 29*7*(5/29) - 29*3y= 29*19 }}}
OK, now rewrite it this way:
(2) {{{ (29/29)*7*5 - 87y = 551 }}}
Notice that {{{ 29/29 = 1 }}}, so
(2) {{{ 35 - 87y = 551 }}}
Subtract {{{35}}} from both sides
(2) {{{ -87y = 516 }}}
Divide both sides by {{{-87}}}
(2) {{{ y = -516/87 }}}
( It doesn't reduce any more )
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Now I have to check the answers
I'll do it on my calculator with approximate decimals
{{{ 5/29 = .172414 }}}
{{{ -516/87 = -5.93103 }}}
I can write:
(1) {{{ 5x+2y=-11 }}}
(1) {{{ 5*.172414 + 2*(-5.93103) = -11 }}}
(1) {{{ .86207 - 11.86207 = -11 }}}
(1) {{{ -11 = -11 }}}
Perfect! Usually there's a slight error due 
to rounding off.
Now you can check the other equation the same way.