SOLUTION: Could someone show me how to work a few problems on the substitution method? 1) x + y = 15 4x + 3y = 38 2) -3x + y = -4 x - y = 0 I have the directions on

Algebra ->  Expressions-with-variables -> SOLUTION: Could someone show me how to work a few problems on the substitution method? 1) x + y = 15 4x + 3y = 38 2) -3x + y = -4 x - y = 0 I have the directions on       Log On


   

Question 145330: Could someone show me how to work a few problems on the substitution method?
1) x + y = 15
4x + 3y = 38

2) -3x + y = -4
x - y = 0
I have the directions on how to work these,but I'm confused on how to write them down onto the paper.If you wouldn't mind showing me,that would help me so much to understand what I'm doing so when I have to take a test in the future.Thank you so much in advance Elle J
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!


Jump to problem # 2
# 1

Start with the given system of equations:

system%28x%2By=15%2C4x%2B3y=38%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=15 Start with the first equation


y=15-x Subtract x from both sides


y=-x%2B15 Rearrange the equation



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

Since y=-x%2B15, we can now replace each y in the second equation with -x%2B15 to solve for x



4x%2B3highlight%28%28-x%2B15%29%29=38 Plug in y=-x%2B15 into the first equation. In other words, replace each y with -x%2B15. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.



4x%2B%283%29%28-1%29x%2B%283%29%2815%29=38 Distribute 3 to -x%2B15


4x-3x%2B45=38 Multiply


x%2B45=38 Combine like terms on the left side


x=38-45Subtract 45 from both sides


x=-7 Combine like terms on the right side





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


So the first part of our answer is: x=-7









Since we know that x=-7 we can plug it into the equation y=-x%2B15 (remember we previously solved for y in the first equation).



y=-x%2B15 Start with the equation where y was previously isolated.


y=-%28-7%29%2B15 Plug in x=-7


y=7%2B15 Multiply


y=22 Combine like terms



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


So the second part of our answer is: y=22









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

So our answers are:

x=-7 and y=22

which form the point






Jump to problem # 1
# 2

Start with the given system of equations:

system%28-3x%2By=-4%2Cx-y=0%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

-3x%2By=-4 Start with the first equation


y=-4%2B3x Add 3x to both sides


y=%2B3x-4 Rearrange the equation


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

Since y=3x-4, we can now replace each y in the second equation with 3x-4 to solve for x



x-highlight%28%283x-4%29%29=0 Plug in y=3x-4 into the first equation. In other words, replace each y with 3x-4. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.



x-3x%2B4=0 Distribute the negative


-2x%2B4=0 Combine like terms on the left side


-2x=0-4Subtract 4 from both sides


-2x=-4 Combine like terms on the right side


x=%28-4%29%2F%28-2%29 Divide both sides by -2 to isolate x



x=2 Divide





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


So the first part of our answer is: x=2









Since we know that x=2 we can plug it into the equation y=3x-4 (remember we previously solved for y in the first equation).



y=3x-4 Start with the equation where y was previously isolated.


y=3%282%29-4 Plug in x=2


y=6-4 Multiply


y=2 Combine like terms



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


So the second part of our answer is: y=2









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

So our answers are:

x=2 and y=2

which form the point