SOLUTION: question: solve each of the following systems by graphing 3x-6y=9 x-2y=3

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Question 55674: question: solve each of the following systems by graphing
3x-6y=9
x-2y=3
Answer by Earlsdon(6098) About Me  (Show Source):
You can put this solution on YOUR website!
These equations are easier to graph if you put them into the slope-intercept form: y = mx+b
2x-6y+=+9 Add 6y to both sides.
2x+=+6y%2B9 Subtract 9 from both sides.
2x-9+=+6y Finally, divide both sides by 6.
%282%2F6%29x+-+9%2F6+=+y Simplify.
y+=+%281%2F3%29x+-+3%2F2
----------------------
x+-+2y+=+3 Add 2y to both sides.
x+=+2y%2B3 Subtract 3 from both sides.
x+-+3+=+2y Finally, divide both sides by 2.
%281%2F2%29x+-+3%2F2+=+y or
y+=+%281%2F2%29x+-+3%2F2
The graphs are:
graph%28300%2C200%2C-5%2C5%2C-5%2C5%2C%281%2F3%29x-%283%2F2%29%2C%281%2F2%29x-%283%2F2%29%29
As you can see from the graph, the two lines intersect at the point (0, -2/3) so this is the solution.
But also notice that both equations, in their slope-intercept form, have the same y-intercept (that's the b in y = mx+b) which is (0, -2/3).