SOLUTION: 3x+y=-2 2x-y=-3 solve by graphing. Find the intersection.

Algebra ->  Linear-equations -> SOLUTION: 3x+y=-2 2x-y=-3 solve by graphing. Find the intersection.      Log On


   

Question 147289: 3x+y=-2
2x-y=-3
solve by graphing. Find the intersection.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Start with the given system of equations:


system%283x%2By=-2%2C2x-y=-3%29


In order to graph these equations, we must solve for y first.


Let's graph the first equation:


3x%2By=-2 Start with the first equation.


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


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


Now let's graph the equation:


Graph of y=-3x-2.


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Now let's graph the second equation:


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


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


y=%28-3-2x%29%2F%28-1%29 Divide both sides by -1 to isolate y.


y=2x%2B3 Rearrange the terms and simplify.


Now let's graph the equation:


Graph of y=2x%2B3.


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Now let's graph the two equations together:


Graph of y=-3x-2 (red). Graph of y=2x%2B3 (green)


From the graph, we can see that the two lines intersect at the point . So the solution to the system of equations is . This tells us that the system of equations is consistent and independent.