SOLUTION: I need help, this problem deals with the substitution method. Your help will be greatly appreciated. x + y = 20 30x + 25y = 550

Algebra ->  Expressions-with-variables -> SOLUTION: I need help, this problem deals with the substitution method. Your help will be greatly appreciated. x + y = 20 30x + 25y = 550       Log On


   

Question 134113: I need help, this problem deals with the substitution method. Your help will be greatly appreciated.
x + y = 20
30x + 25y = 550
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%2By=20%2C30x%2B25y=550%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 first equation

x%2By=20 Start with the first equation


y=20-x Subtract x from both sides


y=-x%2B20 Rearrange the equation


y=%28-x%2B20%29%2F%281%29 Divide both sides by 1


y=%28%28-1%29%2F%281%29%29x%2B%2820%29%2F%281%29 Break up the fraction


y=-x%2B20 Reduce



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

Since y=-x%2B20, we can now replace each y in the second equation with -x%2B20 to solve for x



30x%2B25highlight%28%28-x%2B20%29%29=550 Plug in y=-x%2B20 into the first equation. In other words, replace each y with -x%2B20. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.



30x%2B%2825%29%28-1%29x%2B%2825%29%2820%29=550 Distribute 25 to -x%2B20


30x-25x%2B500=550 Multiply


5x%2B500=550 Combine like terms on the left side


5x=550-500Subtract 500 from both sides


5x=50 Combine like terms on the right side


x=%2850%29%2F%285%29 Divide both sides by 5 to isolate x



x=10 Divide





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


So the first part of our answer is: x=10









Since we know that x=10 we can plug it into the equation y=-x%2B20 (remember we previously solved for y in the first equation).



y=-x%2B20 Start with the equation where y was previously isolated.


y=-%2810%29%2B20 Plug in x=10


y=-10%2B20 Multiply


y=10 Combine like terms



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


So the second part of our answer is: y=10









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

So our answers are:

x=10 and y=10

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%2By=20 (red) and 30x%2B25y=550 (green) and the intersection of the lines (blue circle).