SOLUTION: find the ordered pair solution to the following: 2x + 3y = 12 & 10x + 3y = -12

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: find the ordered pair solution to the following: 2x + 3y = 12 & 10x + 3y = -12      Log On


   



Question 944769: find the ordered pair solution to the following: 2x + 3y = 12 & 10x + 3y = -12
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

2x+%2B+3y+=+12
10x+%2B+3y+=+-12
--------------------

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



Start with the given system of equations:


2x%2B3y=12

10x%2B3y=-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


2x%2B3y=12 Start with the given equation



3y=12-2x Subtract 2+x from both sides



3y=-2x%2B12 Rearrange the equation



y=%28-2x%2B12%29%2F%283%29 Divide both sides by 3



y=%28-2%2F3%29x%2B%2812%29%2F%283%29 Break up the fraction



y=%28-2%2F3%29x%2B4 Reduce



Now lets graph y=%28-2%2F3%29x%2B4 (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+%28-2%2F3%29x%2B4%29+ Graph of y=%28-2%2F3%29x%2B4




So let's solve for y on the second equation


10x%2B3y=-12 Start with the given equation



3y=-12-10x Subtract 10+x from both sides



3y=-10x-12 Rearrange the equation



y=%28-10x-12%29%2F%283%29 Divide both sides by 3



y=%28-10%2F3%29x%2B%28-12%29%2F%283%29 Break up the fraction



y=%28-10%2F3%29x-4 Reduce





Now lets add the graph of y=%28-10%2F3%29x-4 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%28-2%2F3%29x%2B4%2C%28-10%2F3%29x-4%29+ Graph of y=%28-2%2F3%29x%2B4(red) and y=%28-10%2F3%29x-4(green)


From the graph, we can see that the two lines intersect at the point (-3,6) (note: you might have to adjust the window to see the intersection)