SOLUTION: how to solve this 2x+3y=17

Question 529222: how to solve this 2x+3y=17
Answer by lmeeks54(111) (Show Source): You can put this solution on YOUR website!
This equation will be a straight line. The easiest way to figure out where the line is and which way it is headed is to solve it for possible x's and y's. The easiest way to do that is to set either (eventually, both) x or y = 0 and solve for the other quantity.
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The benefit of this is:
-- where x = 0 is the y - intercept (where the line crosses the y axis)
-- where y = 0 is the x - intercept (where the line crosses the x axis)
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Therefore, solve the equation twice, with x = 0 (this provides a point: 0, y) and y = 0 (this provides the point: x, 0). With these two points plotted on a graph, you can draw a line the connects them and extends forever in both directions.
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2(0) + 3y = 17
3y = 17
y = 17/3
y = 5.67
This provides the point, (0, 5.67)
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2x + 3(0) = 17
2x = 17
x = 17/2
x = 8.5
This provides the point, (8.5, 0)
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With these two points, we can examine this graphically (as mentioned above), or use these to points to compute the rise/run to determine the slope...
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and, recalling the general linear equation: y = mx + b, where:
m = the slope and
b = the y intercept
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we can solve this way.
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Of course, we could also have rearranged the original equation, 2x + 3y = 17 into the form, y = mx + b without our discussion of determining the two intercepts, and computing the slope based upon those two points:
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2x + 3y = 17
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subtract 2x from both sides:
3y = -2x + 17
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divide both sides by 3:
y = -2/3 * x + 17/3
y = -0.67x + 5.67
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We can check our earlier work by substituting in the two intercept points we determined previously:
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if we plug in x = 0, we again get y = 5.67 ... that checks
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if we plug in y = 0, we again get x = 8.5 ... that checks too.
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cheers,
Lee
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