Question 1007851

Solve the system of equations through elimination.
{{{2x-3y=21}}}.....eq.1.........both sides multiply by {{{3}}}
{{{-6x+2y=7}}}.........eq.2
-----------------------------

{{{6x-9y=63}}}.....eq.1
{{{-6x+2y=7}}}.........eq.2
-----------------------------add both eq.1 and eq.2

{{{6x-9y+(-6x+2y)=63+7}}}

{{{cross(6x)-9y-cross(6x)+2y=70}}}.......eliminate {{{6x}}} and {{{-6x}}}

{{{-9y+2y=70}}}

{{{-7y=70}}}

{{{y=70/-7}}}

{{{highlight(y= -10)}}}

now go back to {{{-6x+2y=7}}}.........eq.2, substitute {{{-10}}} for {{{y}}} and find {{{x}}}

{{{-6x+2(-10)=7}}}

{{{-7-20=6x}}}

{{{-27=6x}}}

{{{x=-27/6}}}

{{{highlight(x=-9/2)}}} or {{{highlight(x=-4.5)}}}

so, these two lines intersect at point ({{{-4.5}}},{{{-10}}})

{{{drawing( 600, 600, -10, 10, -15, 10, 
circle(-4.5,-10,.12),locate(-4.5,-10,p(-4.5,-10)),
graph( 600, 600, -10, 10, -15, 10, 6x/9-63/9,3x+7/2)) }}}