Question 1010075


{{{2x+4y=30 }}} 
{{{-2x-2y=-21.5 }}}

here you are given two linear equations ( both graph is a line)

you need to solve this system and find {{{x}}} and {{{y}}} value that makes both equations true



{{{2x+4y=30 }}} 
{{{-2x-2y=-21.5 }}}
--------------------add both to eliminate one unknown variable, in your case you can eliminate {{{2x}}} and {{{-2x}}}

{{{2x+4y+(-2x-2y)=30 +(-21.5)}}} 

{{{cross(2x)+4y-cross(2x)-2y=30 -21.5}}} 

{{{4y-2y=8.5}}} 

{{{2y=8.5}}} 

{{{y=8.5/2}}} 

{{{y=4.25}}} 

now, go back to {{{2x+4y=30 }}}, substitute {{{4.25}}} for {{{y}}} and solve for {{{x}}}

{{{2x+4*4.25=30 }}}

{{{2x+17=30 }}}

{{{2x=30 -17}}}

{{{2x=13}}}

{{{x=13/2}}}

{{{x=6.5}}}

so, your lines are intersecting in one point and that point is:

({{{6.5}}},{{{4.25}}})


let's see it on a graph:


 {{{drawing( 600,600, -10,10, -10, 10,
circle(6.5,4.25,.12),locate(6.5,4.25,p(6.5,4.25)),
 graph( 600,600, -10,10, -10, 10, -(1/2)x+7.5,-x+21.5/2)) }}}