SOLUTION: use the graphing method to solve the linear system and tell how many solutions the system has x-7y=10 -6x+4y=-22

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Question 132037: use the graphing method to solve the linear system and tell how many solutions the system has
x-7y=10
-6x+4y=-22
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!


Start with the given system of equations:

1x-7y=10
-6x%2B4y=-22




In order to graph these equations, we need to solve for y for each equation.



So let's solve for y on the first equation

1x-7y=10 Start with the given equation


-7y=10-x Subtract +x from both sides


-7y=-x%2B10 Rearrange the equation


y=%28-x%2B10%29%2F%28-7%29 Divide both sides by -7


y=%28-1%2F-7%29x%2B%2810%29%2F%28-7%29 Break up the fraction


y=%281%2F7%29x-10%2F7 Reduce


Now lets graph y=%281%2F7%29x-10%2F7 (note: if you need help with graphing, check out this solver)


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%281%2F7%29x-10%2F7%29+ Graph of y=%281%2F7%29x-10%2F7



So let's solve for y on the second equation

-6x%2B4y=-22 Start with the given equation


4y=-22%2B6x Add 6+x to both sides


4y=%2B6x-22 Rearrange the equation


y=%28%2B6x-22%29%2F%284%29 Divide both sides by 4


y=%28%2B6%2F4%29x%2B%28-22%29%2F%284%29 Break up the fraction


y=%283%2F2%29x-11%2F2 Reduce



Now lets add the graph of y=%283%2F2%29x-11%2F2 to our first plot to get:

Graph of y=%281%2F7%29x-10%2F7(red) and y=%283%2F2%29x-11%2F2(green)

From the graph, we can see that the two lines intersect at the point (3,-1)