SOLUTION: Solve the system of equations by graphing. then classify the system as consistant of inconsistant and the equalities as dependant or independant. 7x+y=12 8x+9y=-57 What is the

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: Solve the system of equations by graphing. then classify the system as consistant of inconsistant and the equalities as dependant or independant. 7x+y=12 8x+9y=-57 What is the      Log On


   

Question 146683: Solve the system of equations by graphing. then classify the system as consistant of inconsistant and the equalities as dependant or independant.
7x+y=12
8x+9y=-57
What is the solution of the system of equalities
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%287x%2By=12%2C8x%2B9y=-57%29


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


Let's graph the first equation:


7x%2By=12 Start with the first equation.


y=12-7x Subtract 7x from both sides.


y=-7x%2B12 Rearrange the terms and simplify.


Now let's graph the equation:


Graph of y=-7x%2B12.


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Now let's graph the second equation:


8x%2B9y=-57 Start with the second equation.


9y=-57-8x Subtract 8x from both sides.


y=%28-57-8x%29%2F%289%29 Divide both sides by 9 to isolate y.


y=-%288%2F9%29x-19%2F3 Rearrange the terms and simplify.


Now let's graph the equation:


Graph of y=-%288%2F9%29x-19%2F3.


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Now let's graph the two equations together:


Graph of y=-7x%2B12 (red). Graph of y=-%288%2F9%29x-19%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.