SOLUTION: Solve the system of equation by graphing. Then classify the system as consistent or inconsistent and the equation as dependent or independent. 3x+y=16 4x+5y=14

Algebra ->  Graphs -> SOLUTION: Solve the system of equation by graphing. Then classify the system as consistent or inconsistent and the equation as dependent or independent. 3x+y=16 4x+5y=14      Log On


   

Question 147952: Solve the system of equation by graphing. Then classify the system as consistent or inconsistent and the equation as dependent or independent.

3x+y=16
4x+5y=14
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=16%2C4x%2B5y=14%29


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


Let's graph the first equation:


3x%2By=16 Start with the first equation.


y=16-3x Subtract 3x from both sides.


y=-3x%2B16 Rearrange the terms and simplify.


Now let's graph the equation:


Graph of y=-3x%2B16.


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


Now let's graph the second equation:


4x%2B5y=14 Start with the second equation.


5y=14-4x Subtract 4x from both sides.


y=%2814-4x%29%2F%285%29 Divide both sides by 5 to isolate y.


y=-%284%2F5%29x%2B14%2F5 Rearrange the terms and simplify.


Now let's graph the equation:


Graph of y=-%284%2F5%29x%2B14%2F5.


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


Now let's graph the two equations together:


Graph of y=-3x%2B16 (red). Graph of y=-%284%2F5%29x%2B14%2F5 (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.