SOLUTION: 3x+y=5 -2x+3y=4 Solve by graphing

Algebra ->  Graphs -> SOLUTION: 3x+y=5 -2x+3y=4 Solve by graphing      Log On


   

Question 149238: 3x+y=5
-2x+3y=4
Solve by graphing
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Start with the given system of equations:


system%283x%2By=5%2C-2x%2B3y=4%29


In order to graph these equations, we must solve for y first.


Let's graph the first equation:


3x%2By=5 Start with the first equation.


y=5-3x Subtract 3x from both sides.


y=-3x%2B5 Rearrange the terms and simplify.


Now let's graph the equation:


Graph of y=-3x%2B5.


-------------------------------------------------------------------


Now let's graph the second equation:


-2x%2B3y=4 Start with the second equation.


3y=4%2B2x Add 2x to both sides.


y=%284%2B2x%29%2F%283%29 Divide both sides by 3 to isolate y.


y=%282%2F3%29x%2B4%2F3 Rearrange the terms and simplify.


Now let's graph the equation:


Graph of y=%282%2F3%29x%2B4%2F3.


-------------------------------------------------------------------


Now let's graph the two equations together:


Graph of y=-3x%2B5 (red). Graph of y=%282%2F3%29x%2B4%2F3 (green)


From the graph, we can see that the two lines intersect at the point . So the solution to the system of equations is . This tells us that the system of equations is consistent and independent.