Question 190104
we have the given equations as :

{{{ 2x + 3y = -4 }}} ........ (1)

{{{ x - 2y = 5 }}} ............(2)

from equation (2) we extract x in terms of y and we get:

{{{ x - 2y = 5 }}} 

Now, add 2y to both sides of the equation, such that 2y on the left hand side cancels out.

=> {{{ x - cross(2y) + cross(2y) = 2y + 5 }}} 
=> {{{ x = 2y + 5 }}} ............(3)

substitute , this value of x into the first equation (1) . we get:

{{{ 2x + 3y = -4 }}}
=> {{{ 2(2y + 5) + 3y = -4 }}} (use distributive law to open the brackets)
=> {{{ 4y + 10 + 3y = -4 }}} (now, combine the like terms)
=> {{{ 7y + 10 = -4 }}} (Subtract 10 from both sides)
=> {{{ 7y = -4 - 10 }}} 
=> {{{ 7y = -14 }}}
=> {{{ y = -14/7 }}}
=> {{{ highlight(y = -2) }}}

now plug in this value of y, into the equation (3) to get the value of x,

=> {{{ x = 2y + 5 }}}
=> {{{ x = 2(-2) + 5 }}}
=> {{{ x = -4 + 5 }}}
=> {{{ highlight(x = 1) }}}

Checking plug in values of x and y in both equations and verify:

In Equation (1)

{{{ 2x + 3y = -4 }}}
=> {{{ 2(1) + 3(-2) = -4 }}}
=> {{{ 2 - 6 = -4 }}}
=> {{{ -4 = -4 }}}, which is true.

In Equation (2)

{{{ x - 2y = 5 }}}
=> {{{ (1) - 2(-2) = 5 }}}
=> {{{ 1 - (-4) = 5 }}}
=> {{{ 1 + 4 = 5 }}}
=> {{{ 5 = 5 }}}, which is again true,

Hence our answers are correct !

Hope this helps.