SOLUTION: NEED HELP PLEASE!!!! solve by graphing x-2y=-8 3x+4y=6

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Question 169652: NEED HELP PLEASE!!!!
solve by graphing
x-2y=-8
3x+4y=6
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%28x-2y=-8%2C3x%2B4y=6%29


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


Let's graph the first equation:


x-2y=-8 Start with the first equation.


-2y=-8-x Subtract x from both sides.


y=%28-8-x%29%2F%28-2%29 Divide both sides by -2 to isolate y.


y=%281%2F2%29x%2B4 Rearrange the terms and simplify.


Now let's graph the equation:


Graph of y=%281%2F2%29x%2B4.


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Now let's graph the second equation:


3x%2B4y=6 Start with the second equation.


4y=6-3x Subtract 3x from both sides.


y=%286-3x%29%2F%284%29 Divide both sides by 4 to isolate y.


y=-%283%2F4%29x%2B3%2F2 Rearrange the terms and simplify.


Now let's graph the equation:


Graph of y=-%283%2F4%29x%2B3%2F2.


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Now let's graph the two equations together:


Graph of y=%281%2F2%29x%2B4 (red). Graph of y=-%283%2F4%29x%2B3%2F2 (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.