SOLUTION: Need help with solving each system by graphing. Appreciate any assistance. Dont understand it at all. y = -x + 2 y = x - 4 and...... y= -1/4x - 1 y= 3/4x + 3

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons  -> Linear Equations Lesson -> SOLUTION: Need help with solving each system by graphing. Appreciate any assistance. Dont understand it at all. y = -x + 2 y = x - 4 and...... y= -1/4x - 1 y= 3/4x + 3      Log On


   

Question 395928: Need help with solving each system by graphing. Appreciate any assistance. Dont understand it at all.
y = -x + 2
y = x - 4
and......
y= -1/4x - 1
y= 3/4x + 3
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

1.
y+=+-x+%2B+2
y+=+x+-+4.........write in standard form

x+%2B+y+=++2
-x+%2B+y+=+-+4


Solved by pluggable solver: Solve the System of Equations by Graphing



Start with the given system of equations:


1x%2By=2

-x%2By=-4





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%2By=2 Start with the given equation



1y=2-x Subtract +x from both sides



1y=-x%2B2 Rearrange the equation



y=%28-x%2B2%29%2F%281%29 Divide both sides by 1



y=%28-1%2F1%29x%2B%282%29%2F%281%29 Break up the fraction



y=-x%2B2 Reduce



Now lets graph y=-x%2B2 (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+-x%2B2%29+ Graph of y=-x%2B2




So let's solve for y on the second equation


-x%2By=-4 Start with the given equation



1y=-4%2Bx Add +x to both sides



1y=%2Bx-4 Rearrange the equation



y=%28%2Bx-4%29%2F%281%29 Divide both sides by 1



y=%28%2B1%2F1%29x%2B%28-4%29%2F%281%29 Break up the fraction



y=x-4 Reduce





Now lets add the graph of y=x-4 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-x%2B2%2Cx-4%29+ Graph of y=-x%2B2(red) and y=x-4(green)


From the graph, we can see that the two lines intersect at the point (3,-1) (note: you might have to adjust the window to see the intersection)



2.
y=+-%281%2F4%29x+-+1
y=+%283%2F4%29x+%2B+3........write in standard form

%281%2F4%29x+%2B+y=+-+1
-+%283%2F4%29x+%2B+y=+3

Solved by pluggable solver: Solve the System of Equations by Graphing


Let's look at the first equation %281%2F4%29x%2By=-1



4%28%281%2F4%29x%2By%29=4%28-1%29 Multiply both sides of the first equation by the LCD 4



1x%2B4y=-4 Distribute



---------



Let's look at the second equation %28-3%2F4%29x%2By=3


4%28%28-3%2F4%29x%2By%29=4%283%29 Multiply both sides of the second equation by the LCD 4



-3x%2B4y=12 Distribute



---------




So our new system of equations is:


1x%2B4y=-4

-3x%2B4y=12





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%2B4y=-4 Start with the given equation



4y=-4-x Subtract +x from both sides



4y=-x-4 Rearrange the equation



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



y=%28-1%2F4%29x%2B%28-4%29%2F%284%29 Break up the fraction



y=%28-1%2F4%29x-1 Reduce



Now lets graph y=%28-1%2F4%29x-1 (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+%28-1%2F4%29x-1%29+ Graph of y=%28-1%2F4%29x-1




So let's solve for y on the second equation


-3x%2B4y=12 Start with the given equation



4y=12%2B3x Add 3+x to both sides



4y=%2B3x%2B12 Rearrange the equation



y=%28%2B3x%2B12%29%2F%284%29 Divide both sides by 4



y=%28%2B3%2F4%29x%2B%2812%29%2F%284%29 Break up the fraction



y=%283%2F4%29x%2B3 Reduce





Now lets add the graph of y=%283%2F4%29x%2B3 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%28-1%2F4%29x-1%2C%283%2F4%29x%2B3%29+ Graph of y=%28-1%2F4%29x-1(red) and y=%283%2F4%29x%2B3(green)


From the graph, we can see that the two lines intersect at the point (-4,0) (note: you might have to adjust the window to see the intersection)