SOLUTION: How to solve 3x+y=2 with substatution of 4x+y=20????

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Question 395438: How to solve 3x+y=2 with substatution of 4x+y=20????
Found 3 solutions by jim_thompson5910, stanbon, MathLover1:
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%2By=2%2C4x%2By=20%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=2 Start with the first equation


y=2-3x Subtract 3x from both sides


y=-3x%2B2 Rearrange the equation


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

Since y=-3x%2B2, we can now replace each y in the second equation with -3x%2B2 to solve for x



4x%2Bhighlight%28%28-3x%2B2%29%29=20 Plug in y=-3x%2B2 into the second equation. In other words, replace each y with -3x%2B2. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.



x%2B2=20 Combine like terms on the left side


x=20-2Subtract 2 from both sides


x=18 Combine like terms on the right side





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


So the first part of our answer is: x=18









Since we know that x=18 we can plug it into the equation y=-3x%2B2 (remember we previously solved for y in the first equation).



y=-3x%2B2 Start with the equation where y was previously isolated.


y=-3%2818%29%2B2 Plug in x=18


y=-54%2B2 Multiply


y=-52 Combine like terms



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


So the second part of our answer is: y=-52









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

So our answers are:

x=18 and y=-52

which form the point


So the system is both consistent and independent.


If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my tutoring website

Jim

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
How to solve 3x+y=2 with substitution of 4x+y=20
---
Solve for "y":
y = 2-3x
---
Sustitute for "y" and solve for "x":
===
4x+y = 20
4x+(2-3x) = 20
x+2 = 20
x = 18
=====
Solve for "y":
y = 2-3x
y = 2-3*18
y = 2-54
y = -52
=================
cheers,
Stan H.
==========

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

3x%2By=2
4x%2By=20
---------------solve this system with substitution

Solved by pluggable solver: SOLVE linear system by SUBSTITUTION
Solve:
+system%28+%0D%0A++++3%5Cx+%2B+1%5Cy+=+2%2C%0D%0A++++4%5Cx+%2B+1%5Cy+=+20+%29%0D%0A++We'll use substitution. After moving 1*y to the right, we get:
3%2Ax+=+2+-+1%2Ay, or x+=+2%2F3+-+1%2Ay%2F3. Substitute that
into another equation:
4%2A%282%2F3+-+1%2Ay%2F3%29+%2B+1%5Cy+=+20 and simplify: So, we know that y=-52. Since x+=+2%2F3+-+1%2Ay%2F3, x=18.

Answer: system%28+x=18%2C+y=-52+%29.