SOLUTION: Solve the system by the substitution method 4x + y = 25 3x + 4y= 22 the answer the teacher got was 5,10 but I can not figure out how to get there.

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: Solve the system by the substitution method 4x + y = 25 3x + 4y= 22 the answer the teacher got was 5,10 but I can not figure out how to get there.      Log On


   

Question 662280: Solve the system by the substitution method
4x + y = 25
3x + 4y= 22
the answer the teacher got was 5,10
but I can not figure out how to get there.
Found 3 solutions by Alan3354, MathLover1, htmentor:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Solve the system by the substitution method
4x + y = 25 --> y = 25 - 4x
3x + 4y= 22
-------------
Sub for y in the 2nd eqn
3x + 4*(25-4x) = 22
3x + 100 - 16x = 22
-13x = -78
x = 6
------
y = 25-4x
y = 1
--> (6,1)
============
If you sub (5,10), you'll see it doesn't fit

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

4x+%2B+y+=+25........1
3x+%2B+4y=+22.........2
_______________________________
4x+%2B+y+=+25........1..solve for y
y+=+25-4x.........substitute in 2

3x+%2B+4%2825-4x%29=+22.........2..solve for x
3x+%2B+100-16x=+22
+100-13x=+22

+100-22=+13x

+78=+13x

+78%2F13=+x
++highlight%28x=6%29
now find y

y+=+25-4x
y+=+25-4%2A6
y+=+25-24
highlight%28y+=1%29




Answer by htmentor(1343) About Me  (Show Source):
You can put this solution on YOUR website!
Solve the system by the substitution method
4x + y = 25
3x + 4y= 22
=============================
Solve for y in the 1st equation:
y = 25 - 4x
Substitute the value for y in the 2nd equation:
3x + 4(25-4x) = 22
3x + 100 - 16x = 22
13x = 78
x = 6
So y = 25 - 4*6 = 1
Ans: x=6, y=1