SOLUTION: Hi, I have a problem here, I am horrible with math so please go easy on me. I don't even know if this is in the right category. My paper says Solving System of Equations by Graph

Algebra ->  Systems-of-equations -> SOLUTION: Hi, I have a problem here, I am horrible with math so please go easy on me. I don't even know if this is in the right category. My paper says Solving System of Equations by Graph      Log On


   

Question 1154404: Hi, I have a problem here, I am horrible with math so please go easy on me. I don't even know if this is in the right category. My paper says
Solving System of Equations by Graphing
y = -2x+6
y=2x+2
They are in the same problem.
Thank you for the help and for taking the time to read this.
Found 3 solutions by MathLover1, ikleyn, MathTherapy:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

y+=+-2x%2B6
y=2x%2B2
-----------------------
rewrite in standard form:

2x%2By+=+6
-2x%2By=2
-------------

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



Start with the given system of equations:


2x%2By=6

-2x%2By=2





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


2x%2By=6 Start with the given equation



1y=6-2x Subtract 2+x from both sides



1y=-2x%2B6 Rearrange the equation



y=%28-2x%2B6%29%2F%281%29 Divide both sides by 1



y=%28-2%2F1%29x%2B%286%29%2F%281%29 Break up the fraction



y=-2x%2B6 Reduce



Now lets graph y=-2x%2B6 (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+-2x%2B6%29+ Graph of y=-2x%2B6




So let's solve for y on the second equation


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



1y=2%2B2x Add 2+x to both sides



1y=%2B2x%2B2 Rearrange the equation



y=%28%2B2x%2B2%29%2F%281%29 Divide both sides by 1



y=%28%2B2%2F1%29x%2B%282%29%2F%281%29 Break up the fraction



y=2x%2B2 Reduce





Now lets add the graph of y=2x%2B2 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-2x%2B6%2C2x%2B2%29+ Graph of y=-2x%2B6(red) and y=2x%2B2(green)


From the graph, we can see that the two lines intersect at the point (1,4) (note: you might have to adjust the window to see the intersection)

Answer by ikleyn(52776) About Me  (Show Source):
You can put this solution on YOUR website!
.

In this system of equations, the left sides are identical.

Hence, right sides are equal


    -2x + 6 = 2x + 2.


Thus you have one single equation for the unknown "x" only.


From the equation


    6 - 2 = 2x + 2x

    4     = 4x

    x     = 4/4 = 1.


Thus one unknown is just found :  x= 1.


Now substitute it into either of the two original equations.


The easiest way is to substitute it into the second equation to get


    y = 2x+2 = 2*1 + 2 = 4.


ANSWER.  The solution to the system is  x= 1, y =4.

Solved.



Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!
Hi, I have a problem here, I am horrible with math so please go easy on me. I don't even know if this is in the right category. My paper says
Solving System of Equations by Graphing
y = -2x+6
y=2x+2
They are in the same problem.
Thank you for the help and for taking the time to read this.
Pay ABSOLUTELY no attention to what the other person posted!
This problem is NOT CLOSE to being so complex, because it's one of those that you can easily find the INTERCEPTS (x and y), and join them to get the 2 lines.

y = - 2x + 6
Finding the x-intercept by substituting 0 for y
0 = - 2x + 6
2x = 6
matrix%281%2C5%2C+x%2C+%22=%22%2C+6%2F2%2C+%22=%22%2C+3%29
x-intercept: (3, 0)

y = - 2x + 6
Finding the y-intercept by substituting 0 for x
y = - 2(0) + 6
y = 6
y-intercept: (0, 6)
Now, plot these points on the x and the y intercepts, and draw a line through them. You just drew the line of the equation: y = - 2x + 6
=======================================================================================================================
y = 2x + 2
Finding the x-intercept by substituting 0 for y
0 = 2x + 2
- 2 = 2x
matrix%281%2C5%2C+x%2C+%22=%22%2C+%28-+2%29%2F2%2C+%22=%22%2C+-+1%29
x-intercept: (- 1, 0)

y = 2x + 2
Finding the y-intercept by substituting 0 for x
y = 2(0) + 2
y = 2
y-intercept: (0, 2)
Now, plot these points on the x and the y intercepts, and draw a line through them. You just drew the line of the equation: y = 2x + 2
Check to see where the 2 line graphs intersect. That's your solution to the system!!

You're DONE!!