Question 463148
Which pair of equations does NOT have a common solution?
a) 

{{{x+y = -1}}}; {{{4x-3y=24}}}

b){{{4x+6y=12}}}; {{{6x+9y=12}}}

c) {{{2x-3y=-4}}}; {{{2x+y=4}}}

d) {{{5x-4y=9}}}; {{{x-2y=-3}}}

easiest way is to write all of them in slope-intercept form and see if any of them are parallel lines; parallel lines do NOT have a common solution


a) 

{{{y =-x-1}}}...slope is {{{-1}}} 

{{{4x-24=3y}}}

{{{(4/3)x-8=y}}}..slope is {{{(4/3)}}}


b)

{{{4x+6y=12}}}...{{{6y=-4x+12}}}...{{{y=-(4/6)x+2}}}.{{{y=-(2/3)x+2}}}...slope is {{{-(2/3)}}}


{{{6x+9y=12}}}.....{{{9y=-6x+12}}}...{{{y=-(6/9)x+12/9}}}...{{{y=-(2/3)x+4/3}}}...slope is {{{-(2/3)}}}


c) 

{{{2x-3y=-4}}} .....{{{2x+4=3y}}} .....{{{(2/3)x+4/3=y}}} ...slope is {{{(2/3)}}}

{{{2x+y=4}}}...{{{y=-2x+4}}}...slope is {{{-2}}}



d) 
{{{5x-4y=9}}}....{{{5x-9=4y}}}...{{{(5/4)x-9/4=y}}}..slope is {{{(5/4)}}}

 {{{x-2y=-3}}}.....{{{x+3=2y}}}.....{{{(1/2)x+3/2=y}}}.slope is {{{(1/2)}}}

as you can see, only 

b)

{{{4x+6y=12}}} and {{{6x+9y=12}}} have same slope..

let's see if these lines are parallel:

{{{ graph( 500, 500, -10, 10, -10, 10, -(2/3)x+2,-(2/3)x+4/3) }}}


so, your answer is {{{b}}}