Question 164302
Transform both to slope-intercept form and graph.
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{{{x+2y=9}}}
{{{2y=9-x}}}
{{{y=(9-x)/2}}}
Slope = -1/2, Y-intercept=9/2
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{{{-x+6y=-1}}} 
{{{6y=x-1}}}
{{{y=(x-1)/6}}}
Slope=1/6, Y-intercept=-1/6 
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Then graph the two lines. 
{{{drawing( 300, 300, -2, 10, -5, 5,grid( 1 ),circle( 7, 1, .2 ), graph( 300, 300, -2, 10, -5, 5, (9-x)/2, (x-1)/6)) }}} 
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Looks like (7,1) is the solution.
Check using the equations. 
{{{x+2y=9}}}
{{{7+2(1)=9}}}
{{{7+2=9}}}
{{{9=9}}}
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{{{-x+6y=-1}}}
{{{-7+6(1)=-1}}}
{{{-7+6=-1}}}
{{{-1=-1}}}
The solution was verified using both equations. 
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Now the algebraic solution.  
1.{{{x+2y=9}}}
2.{{{-x+6y=-1}}}
Add eq. 1 and eq. 2 to get rid of x.
{{{x+2y+(-x)+6y=9-1}}}
{{{8y=8}}}
{{{highlight(y=1)}}}
Then from eq. 1,
1.{{{x+2y=9}}}
{{{x+2(1)=9}}}
{{{highlight(x=7)}}}