SOLUTION: Solve the system of equations by graphing. Then, classify the system. 3x-y=17 3x+4y=7 What is the solution of the system? ______ Is the system consistent or inconsisten

Algebra ->  Graphs -> SOLUTION: Solve the system of equations by graphing. Then, classify the system. 3x-y=17 3x+4y=7 What is the solution of the system? ______ Is the system consistent or inconsisten      Log On


   

Question 161081: Solve the system of equations by graphing. Then, classify the system.
3x-y=17
3x+4y=7
What is the solution of the system? ______
Is the system consistent or inconsistent? ______
Are the equations dependent or independent? _______
Graph your answer to the equation.
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-y=17%2C3x%2B4y=7%29


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


Let's graph the first equation:


3x-y=17 Start with the first equation.


-y=17-3x Subtract 3x from both sides.


y=%2817-3x%29%2F%28-1%29 Divide both sides by -1 to isolate y.


y=3x-17 Rearrange the terms and simplify.


Now let's graph the equation:


Graph of y=3x-17.


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Now let's graph the second equation:


3x%2B4y=7 Start with the second equation.


4y=7-3x Subtract 3x from both sides.


y=%287-3x%29%2F%284%29 Divide both sides by 4 to isolate y.


y=-%283%2F4%29x%2B7%2F4 Rearrange the terms and simplify.


Now let's graph the equation:


Graph of y=-%283%2F4%29x%2B7%2F4.


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Now let's graph the two equations together:


Graph of y=3x-17 (red). Graph of y=-%283%2F4%29x%2B7%2F4 (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.