Question 872791
Find the (x,y) location of the intersection
of the lines:
(1) {{{ x - 2y - 4 = 0 }}}
(2) {{{ 4x - y - 4 = 0 }}}
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Multiply (1) by {{{ 4 }}} and
subtract (1) from (2)
(2) {{{ 4x - y - 4 = 0 }}}
(1) {{{ -4x + 8y + 16 = 0 }}}
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{{{ 7y + 12 = 0 }}}
{{{ y = -12/7 }}}
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Plug this back into (1) or (2)
(1) {{{ x - 2*(-12/7) - 4 = 0 }}}
(1) {{{ x + 24/7 - 28/7 = 0 }}}
(1) {{{ x - 4/7 = 0 }}}
(1) {{{ x = 4/7 }}}
The intersection is at ( 4/7, -12/7 )
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(a) Find the slope of this line
{{{ 16x - 11y + 3 = 0 }}}
{{{ 11y = 16x + 3 }}}
{{{ y = (16/11)*x + 3/11 }}}
The slope is {{{ 16/11 }}}
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You can use the point-slope formula
{{{ ( y - (-12/7) ) / ( x - 4/7 ) = 16/11 }}}
{{{ y + 12/7 = ( 16/11 )*( x - 4/7 ) }}}
{{{ y + 12/7 = (16/11)*x - (16/11)*(4/7) }}}
Multiply both sides by {{{ 77 }}}
{{{ 77y + 11*12 = 7*16*x - 4*16 }}}
{{{ 77y = 112x - 132 - 64 }}}
{{{ 77y = 112x - 196 }}}
{{{ 112x - 77y - 196 = 0 }}}
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That's it unless I made a mistake.
That's all I have time for