Question 174146
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{{{2x-5y=-6 }}}------------>EQN 1, {{{y=(2x+6)/5=(2/5)x+(6/5)}}}
{{{8x+3y=68}}}------------->EQN 2, {{{y=(-8x+68)/3=(-8/3)x+(68/3)}}}
In EQN 1 we get:
{{{2x=5y-6}}}, transpose terms and isolate "x"
{{{cross(2)x/cross(2)=(5y-6)/2}}}, divide the whole eqn by 2
{{{x=(5/2)y-(6/2)=(5/2)y-3}}}--------------> EQN 3
Subst. EQN 3 in EQN 2:
{{{8((5/2)y-3)+3y=68}}}
{{{(40/2)y-24+3y=68}}}
{{{20y-24+3y=68}}}, combine similar terms
{{{23y=68+24=92}}}
{{{cross(23)y/cross(23)=cross(92)4/cross(23)}}}
{{{highlight(y=4)}}}, subst. in EQN 3:
{{{x=(5/2)(4)-3=(20/2)-3=10-3}}}
{{{highlight(x=7)}}}
So the ordered pair -----> (7,4)
Let's see the graph:
{{{drawing(300,300,-9,9,-10,10,grid(1),graph(300,300,-9,9,-10,10,(2/5)x+(6/5),(-8/3)x+(68/3)),blue(circle(7,4,.20)))}}}
Thanky ou,
Jojo</pre>