SOLUTION: I need to solve this problem by the substitution method. I cannot figure out how to get the answer shown in the back of the book. The problem is: x+4y=14 2x-y=1 Here are some

Question 181157: I need to solve this problem by the substitution method. I cannot figure out how to get the answer shown in the back of the book. The problem is:
x+4y=14
2x-y=1
Here are some of the ways I tried to solve it;
x(2x + 1) + 4y = 14
2(14-4y)-y=1
I tried moving the equation around like: y=2x +1 and x=14-4y.
I have spent over 2 hours on this question. The answers in the book are (2,3). Please help!!
Found 3 solutions by Alan3354, stanbon, solver91311:
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
x+4y=14
2x-y=1
Here are some of the ways I tried to solve it;
x(2x + 1) + 4y = 14
2(14-4y)-y=1
I tried moving the equation around like: y=2x +1 and x=14-4y.
I have spent over 2 hours on this question. The answers in the book are (2,3). Please help!!
================
I tried moving the equation around like: y=2x +1 and x=14-4y.
You were on the right track there.
To use substitution, you solve for one of the variables, then sub into the other equation.
Take this one: y=2x +1
and sub for y into the other eqn.
x + 4*(2x+1) = 14
x + 4x+4 = 14
5x = 10
x = 2
---------------
That's one. Then sub 2 for x into either eqn.
2x-y=1
2*2 - y = 1
4 - y = 1
-y = -3
y = 3

Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
I need to solve this problem by the substitution method. I cannot figure out how to get the answer shown in the back of the book. The problem is:
x+4y=14
2x-y=1
------------------
Solve the 1st for "x":
x = 14-4y
-------
Substitute into 2x-y = 1
2(14-4y) - y = 1
28 -8y -y = 1
-9y = -27
y = 3
-----
The x = 14-4y = 14 - 4*3 = 2
==================================
Cheers,
Stan H.
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!

Works just fine:

Then

Your other way, isn't going to work. You have a sign error.

.

Using this expression to substitute:

And then substituting this value:

Same answer. Your solution set consists of the single ordered pair (2,3).

John

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