Question 238614
I'll get the equations into slope intercept form and let you do the graphing.




{{{x+2y=6}}} Start with the first equation.



{{{2y=6-x}}} Subtract {{{x}}} from both sides.



{{{2y=-x+6}}} Rearrange the terms.



{{{y=(-x+6)/(2)}}} Divide both sides by {{{2}}} to isolate y.



{{{y=((-1)/(2))x+(6)/(2)}}} Break up the fraction.



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



So the equation {{{y=-(1/2)x+3}}} is now in slope intercept form {{{y=mx+b}}} where the slope is {{{m=-1/2}}} and the y-intercept is {{{b=3}}} note: the y-intercept is the point *[Tex \LARGE \left(0,3\right)]


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{{{2x+y=9}}} Now move onto the second equation.



{{{y=9-2x}}} Subtract {{{2x}}} from both sides.



{{{y=-2x+9}}} Rearrange the terms.



So the equation {{{y=-2x+9}}} is now in slope intercept form {{{y=mx+b}}} where the slope is {{{m=-2}}} and the y-intercept is {{{b= 9}}} note: the y-intercept is the point *[Tex \LARGE \left(0, 9\right)]