Question 905827
{{{ x - y - 4 = 0 }}}
{{{ 2x + y - 5 = 0 }}}
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Add the equations
{{{ 3x - 9 = 0 }}}
{{{ 3x = 9 }}}
{{{ x = 3 }}}
and
{{{ x - y - 4 = 0 }}}
{{{ 3 - y - 4 = 0 }}}
{{{ y = 3 - 4 }}}
{{{ y = -1 }}}
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The line you need goes through
( 3, -1 )
( 0, 0 )
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Use the general point-slope formula
{{{ ( y - (-1) ) / ( x - 3 ) = ( 0 - (-1) ) / ( 0 - 3 ) }}}
{{{ ( y + 1 ) / ( x - 3 ) = 1 / (-3) }}}
{{{ -3*( y + 1 ) = x - 3 }}}
{{{ -3y - 3 = x - 3 }}}
{{{ x + 3y = 0 }}}
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check:
Does line pass through origin?
{{{ 0 + 3*0 = 0 }}}
OK
Does line pass through ( 3, -1 ) ?
{{{ 3 + 3*(-1)  = 0 }}}
{{{ 3 - 3 = 0 }}}
OK