SOLUTION: Use a graphing calculator to solve the system. (Simplify your answer completely.) 4x + 9y = 4 6x + 3y = −1

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: Use a graphing calculator to solve the system. (Simplify your answer completely.) 4x + 9y = 4 6x + 3y = −1       Log On


   

Question 1130554: Use a graphing calculator to solve the system. (Simplify your answer completely.)
4x + 9y = 4
6x + 3y = −1
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

4x+%2B+9y+=+4
6x+%2B+3y+=+-1

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



Start with the given system of equations:


4x%2B9y=4

6x%2B3y=-1





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


4x%2B9y=4 Start with the given equation



9y=4-4x Subtract 4+x from both sides



9y=-4x%2B4 Rearrange the equation



y=%28-4x%2B4%29%2F%289%29 Divide both sides by 9



y=%28-4%2F9%29x%2B%284%29%2F%289%29 Break up the fraction



y=%28-4%2F9%29x%2B4%2F9 Reduce



Now lets graph y=%28-4%2F9%29x%2B4%2F9 (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+%28-4%2F9%29x%2B4%2F9%29+ Graph of y=%28-4%2F9%29x%2B4%2F9




So let's solve for y on the second equation


6x%2B3y=-1 Start with the given equation



3y=-1-6x Subtract 6+x from both sides



3y=-6x-1 Rearrange the equation



y=%28-6x-1%29%2F%283%29 Divide both sides by 3



y=%28-6%2F3%29x%2B%28-1%29%2F%283%29 Break up the fraction



y=-2x-1%2F3 Reduce





Now lets add the graph of y=-2x-1%2F3 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%28-4%2F9%29x%2B4%2F9%2C-2x-1%2F3%29+ Graph of y=%28-4%2F9%29x%2B4%2F9(red) and y=-2x-1%2F3(green)


From the graph, we can see that the two lines intersect at the point (-1%2F2,2%2F3) (note: you might have to adjust the window to see the intersection)