SOLUTION: solve the system of equations by graphing x-2y=10 x+2y=-2

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Question 146961: solve the system of equations by graphing
x-2y=10
x+2y=-2

Answer by jim_thompson5910(30480) About Me  (Show Source):
You can put this solution on YOUR website!

Start with the given system of equations:


system%28x-2y=10%2Cx%2B2y=-2%29


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


Let's graph the first equation:


x-2y=10 Start with the first equation.


-2y=10-x Subtract x from both sides.


y=%2810-x%29%2F%28-2%29 Divide both sides by -2 to isolate y.


y=%281%2F2%29x-5 Rearrange the terms and simplify.


Now let's graph the equation:


Graph of y=%281%2F2%29x-5.


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Now let's graph the second equation:


x%2B2y=-2 Start with the second equation.


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


y=%28-2-x%29%2F%282%29 Divide both sides by 2 to isolate y.


y=-%281%2F2%29x-1 Rearrange the terms and simplify.


Now let's graph the equation:


Graph of y=-%281%2F2%29x-1.


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Now let's graph the two equations together:


Graph of y=%281%2F2%29x-5 (red). Graph of y=-%281%2F2%29x-1 (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.