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

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) (Show Source): You can put this solution on YOUR website!

Start with the given system of equations:

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

Let's graph the first equation:

Start with the first equation.

Subtract from both sides.

Rearrange the terms and simplify.

Now let's graph the equation:

Graph of .

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

Now let's graph the second equation:

Start with the second equation.

Subtract from both sides.

Divide both sides by to isolate .

Rearrange the terms and simplify.

Now let's graph the equation:

Graph of .

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

Now let's graph the two equations together:

Graph of (red). Graph of (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.

RELATED QUESTIONS
solve the system of equation by graphing. then classify the system as consistent aor... (answered by nabla)

Solve the system of equations by graphing. Then classify the system as consistent or... (answered by jim_thompson5910)

Solve the system of equations by graphing. Then classify the system as consistent or... (answered by oscargut)

solve the system of equations by graphing. Then classify the system as consistent or... (answered by Alan3354)

Solve the system of equations by graphing. Then classify the system as consistent or... (answered by stanbon)

Solve the system of equations by graphing. Then classify the system as consistent or... (answered by Gogonati)

I have one more question. Solve the system of equations by graphing. Then classify the... (answered by jim_thompson5910)

5x-5y=20 5y-5x=-20 solve the system of equtions by graphing. then classify the system (answered by drk,stanbon)