SOLUTION: I have tried this but I am having trouble, can you please help. Use substitution to solve each system. If it does not have one solution then put no solution or indinitely many so

Algebra ->  Expressions-with-variables -> SOLUTION: I have tried this but I am having trouble, can you please help. Use substitution to solve each system. If it does not have one solution then put no solution or indinitely many so      Log On


   

Question 181876: I have tried this but I am having trouble, can you please help. Use substitution to solve each system. If it does not have one solution then put no solution or indinitely many solutions. X-5Y=36 2X+Y=-16
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%28x-5y=36%2C2x%2By=-16%29



Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to solve for y.




So let's isolate y in the second equation

2x%2By=-16 Start with the second equation


y=-16-2x Subtract 2x from both sides


y=-2x-16 Rearrange the equation


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

Since y=-2x-16, we can now replace each y in the second equation with -2x-16 to solve for x



x-5highlight%28%28-2x-16%29%29=36 Plug in y=-2x-16 into the first equation. In other words, replace each y with -2x-16. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.



x%2B%28-5%29%28-2%29x%2B%28-5%29%28-16%29=36 Distribute -5 to -2x-16


x%2B10x%2B80=36 Multiply


11x%2B80=36 Combine like terms on the left side


11x=36-80Subtract 80 from both sides


11x=-44 Combine like terms on the right side


x=%28-44%29%2F%2811%29 Divide both sides by 11 to isolate x



x=-4 Divide





-----------------First Answer------------------------------


So the first part of our answer is: x=-4









Since we know that x=-4 we can plug it into the equation y=-2x-16 (remember we previously solved for y in the first equation).



y=-2x-16 Start with the equation where y was previously isolated.


y=-2%28-4%29-16 Plug in x=-4


y=8-16 Multiply


y=-8 Combine like terms



-----------------Second Answer------------------------------


So the second part of our answer is: y=-8









-----------------Summary------------------------------

So our answers are:

x=-4 and y=-8

which form the point








Now let's graph the two equations (if you need help with graphing, check out this solver)


From the graph, we can see that the two equations intersect at . This visually verifies our answer.




graph of x-5y=36 (red) and 2x%2By=-16 (green) and the intersection of the lines (blue circle).