SOLUTION: I am trying to solve these equations. We are to graph the system and estimate the solution then check the solution algebraically: 2x-3y = -2 x+y = -6 This is what I have don

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: I am trying to solve these equations. We are to graph the system and estimate the solution then check the solution algebraically: 2x-3y = -2 x+y = -6 This is what I have don      Log On


   

Question 253245: I am trying to solve these equations. We are to graph the system and estimate the solution then check the solution algebraically:
2x-3y = -2
x+y = -6
This is what I have done so far and it isn't coming out correctly:
2x-3y = -2
2x+2=3y
2/3x + 2/3 = y
x+y= -6
x+6= -y
I plotted the line at (0,2/3) (3, 2 2/3) and at (-3, -1 1/3)
The book says I am wrong and I don't understand why. Please help!
ANy help you can give would be greatly appreciated. Thank you.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First let's graph 2x-3y+=+-2. To do so, we need to solve for 'y'


2x-3y=-2 Start with the first equation.


-3y=-2-2x Subtract 2x from both sides.


-3y=-2x-2 Rearrange the terms.


y=%28-2x-2%29%2F%28-3%29 Divide both sides by -3 to isolate y.


y=%28%28-2%29%2F%28-3%29%29x%2B%28-2%29%2F%28-3%29 Break up the fraction.


y=%282%2F3%29x%2B2%2F3 Reduce.


Now in order to graph y=%282%2F3%29x%2B2%2F3, we need two points.

Take note that when x=2, then y=%282%2F3%29%282%29%2B2%2F3=4%2F3%2B2%2F3=6%2F3=2. So we have one point (2,2).


Also, when x=5, y=%282%2F3%29%285%29%2B2%2F3=10%2F3%2B2%2F3=12%2F3=4 giving us another point (5,4). Plot these points to get






Now draw a straight line through the two points. This line is the graph of y=%282%2F3%29x%2B2%2F3


Graph of y=%282%2F3%29x%2B2%2F3 through the two points (2,2) and (5,4)


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Now let's graph x%2By+=+-6


x%2By=-6 Start with the second equation.


y=-6-x Subtract x from both sides.


y=-x-6 Rearrange the terms.


Looking at y=-x-6 we can see that the equation is in slope-intercept form y=mx%2Bb where the slope is m=-1 and the y-intercept is b=-6


Since b=-6 this tells us that the y-intercept is .Remember the y-intercept is the point where the graph intersects with the y-axis

So we have one point




Now since the slope is comprised of the "rise" over the "run" this means
slope=rise%2Frun

Also, because the slope is -1, this means:

rise%2Frun=-1%2F1


which shows us that the rise is -1 and the run is 1. This means that to go from point to point, we can go down 1 and over 1



So starting at , go down 1 unit


and to the right 1 unit to get to the next point



Now draw a line through these points to graph y=-x-6



So this is the graph of y=-x-6 through the points and


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Now let's graph the two equations on the same coordinate plane


Graph of y=%282%2F3%29x%2B2%2F3 (red) and y=-x-6 (green)


From the graph, we see that the two lines intersect at the point (-4, -2). So the solutions are x=-4 and y=-2


Check:

2x-3y=-2 Start with the first equation.


2%28-4%29-3%28-2%29=-2 Plug in x=-4 and y=-2


-8%2B6=-2 Multiply


-2=-2 Add. Since the equation is true, this verifies our answer on the first equation.


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x%2By=-6 Move onto the second equation.


-4-2=-6 Plug in x=-4 and y=-2


-6=-6 Subtract. Since the equation is true, this verifies our answer for the second equation.


Since the values x=-4 and y=-2 satisfy both equations, this verifies our answer completely.