Question 488200: Solve each system graphically y = x + 2, 3y − 2x = 4?
I need the problem worked out and explained and graphed if possible. Thank you
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Solve each system graphically y = x + 2, 3y − 2x = 4?
I need the problem worked out and explained and graphed if possible.
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y = x + 2
3y − 2x = 4
Both equations are that of straight lines of the standard form: y=mx+b, m=slope,
b=y-intercept.
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The first equation is already in standard form where the slope=1 and the y-intercept=2.
To graph this line, all you need are two point since the equation is a straight line. You already have one point, the y-intercept=2. To find the second point, start from 2 on the y-axis and move one unit up and one unit to the right (rise/run) or one unit down and one unit to the left connecting the line. As a check, you can plug in an x-value like 3 and see if it falls on the line you drew. For this simple equation already in standard form, it would be just as easy to graph the line by plotting points, but sometimes the equation is not as simple. See the following graph as a check on the answers:
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The second equation is also a straight line but not written in standard form: We should write it in standard before doing anything with it.
3y-2x=4
3y=2x+4
y=(2/3)x+4/3
slope=2/3, y-intercept=4/3
To graph the line, follow the same procedure as above, that is, starting from 4/3 on the y-axis, move 2 units up and 3 units to the right or 2 units down and 3 units to the left to get the second point connecting the line.
See the following graph as a check on the answers:
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