Question 1180577

 

{{{2x - y - 4 = 0}}}.............eq.1
{{{x + 2y + 3 = 0}}} .............eq.2
{{{mx + y - 1 = 0}}}.............eq.3
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start with

{{{2x - y - 4 = 0}}}.............eq.1
{{{x + 2y + 3 = 0}}} .............eq.2...........both sides multiply by {{{2}}}
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{{{2x - y - 4 = 0}}}.............eq.1
{{{2x + 4y + 6 = 0}}} .............eq.2.............subtract
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{{{2x - y - 4-(2x + 4y + 6) = 0}}}
{{{2x - y - 4-2x - 4y - 6 = 0}}}
 {{{- 5y - 10 = 0}}}
 {{{ - 10 = 5y}}}
{{{y=-10/5}}}
{{{y=-2}}}


go to

{{{2x - y - 4 = 0}}}.............eq.1, substitute {{{y}}}
{{{2x - (-2) - 4 = 0}}}
{{{2x +2 - 4 = 0}}}
{{{2x  - 2 = 0}}}
{{{2x  = 2}}}
{{{x=1}}}


go to

{{{mx + y - 1 = 0}}}.............eq.3, substitute {{{x}}} and {{{y}}}
{{{m*1 -2 - 1 = 0}}}
{{{m -3 = 0}}}
{{{m  = 3}}}

third line is

{{{3x + y - 1 = 0}}} 

all three lines intersect at point ({{{1}}},{{{-2}}})

{{{ graph( 600, 600, -10, 10, -10, 10, -3x+1,2x-4,-x/2-3/2) }}}