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

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) (Show Source): You can put this solution on YOUR website!
First let's graph . To do so, we need to solve for 'y'

Start with the first equation.

Subtract from both sides.

Rearrange the terms.

Divide both sides by to isolate y.

Break up the fraction.

Reduce.

Now in order to graph , we need two points.

Take note that when , then . So we have one point (2,2).

Also, when , 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

Graph of through the two points (2,2) and (5,4)

-------------------------------------------------------------------------

Now let's graph

Start with the second equation.

Subtract from both sides.

Rearrange the terms.

Looking at we can see that the equation is in slope-intercept form where the slope is and the y-intercept is

Since 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

Also, because the slope is , this means:

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

So this is the graph of through the points

and

------------------------------------------------------------------------

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

Graph of (red) and (green)

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

Check:

Start with the first equation.

Plug in and

Multiply

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

-------------

Move onto the second equation.

Plug in and

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

Since the values and satisfy both equations, this verifies our answer completely.

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