Question 556013
(1) {{{ y = 4x - 5 }}}
(2) {{{ ( x - 8 )^2 + ( y - (-10) )^2 = ( x - (-7) )^2 + ( y - 0 )^2 }}}
-------------
This is 2 equations and 2 unknowns, so it's solvable
(1) {{{ 4x - y = 5 }}}
and
(2) {{{ ( x - 8 )^2 + ( y + 10 )^2 = ( x + 7 )^2 +  y^2 }}}
(2) {{{ x^2 - 16x + 64 + y^2 + 20y + 100 = x^2 + 14x + 49 + y^2 }}}
(2) {{{ -16x + 20y + 64 + 100 = 14x + 49 }}}
(2) {{{ 14x + 16x - 20y = 164 - 49 }}}
(2) {{{ 30x - 20y = 115 }}}
(2) {{{ 6x - 4y = 23 }}}
Multiply both sides of (1) by {{{4}}} 
and subtract (1) from (2)
(2) {{{ 6x - 4y = 23 }}}
(1) {{{ -16x + 4y = -20 }}}
{{{ -10x = 3 }}}
{{{ x = -(3/10) }}}
and, since
(1) {{{ y = 4x - 5 }}}
(1) {{{ y = -(12/10) - 5 }}}
(1) {{{ y = -(6/5) -(25/5) }}}
(1) {{{ y = -(31/5) }}}
(x,y) = (-3/10, -31/5 )
---------------------
check:
(1) {{{ y = 4x - 5 }}}
(1) {{{ -(31/5) = 4*(-3/10) - 5 }}}
(1) {{{ -(31/5) = -(12/10) - 25/5 }}}
(1) {{{ -(31/5) = -(6/5) -(25/5) }}}
(1) {{{ -(31/5) = -(31/5) }}}
OK
(2) {{{ ( x - 8 )^2 + ( y - (-10) )^2 = ( x - (-7) )^2 + ( y - 0 )^2 }}}
(2) {{{ ( -(3/10) - 8 )^2 + ( -(31/5) - (-10) )^2 = ( -(3/10) - (-7) )^2 + ( -(31/5) - 0 )^2 }}}
(2) {{{ (-83/10)^2 + (19/5)^2 = (67/10)^2 + (-31/5)^2 }}}
(2) {{{ (-83/10)^2 + (38/10)^2 = (67/10)^2 + (-62/10)^2 }}}
(2) {{{ 68.89 + 14.44 = 44.89 + 38.44 }}}
(2) {{{ 83.33 = 83.33 }}}
OK