SOLUTION: Solve the system of equation by graphing? -3x -y = -3 2x + y = 2 What is the solution of the system of equation? (Type an order pair)

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Question 157502: Solve the system of equation by graphing?
-3x -y = -3
2x + y = 2
What is the solution of the system of equation?
(Type an order pair)
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%28-3x-y=-3%2C2x%2By=2%29


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


Let's graph the first equation:


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


-y=-3%2B3x Add 3x to both sides.


y=%28-3%2B3x%29%2F%28-1%29 Divide both sides by -1 to isolate y.


y=-3x%2B3 Rearrange the terms and simplify.


Now let's graph the equation:


Graph of y=-3x%2B3.


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Now let's graph the second equation:


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


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


y=-2x%2B2 Rearrange the terms and simplify.


Now let's graph the equation:


Graph of y=-2x%2B2.


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Now let's graph the two equations together:


Graph of y=-3x%2B3 (red). Graph of y=-2x%2B2 (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.