# Systems of Equations Help

I have a systems of equations word problem that I need help with:

Since my uncles farmyard appears to be overrun with dogs, and chickens, I asked him how many of each he had. He responded that his dogs and chickens had a total of 148 legs and 60 heads. How many dogs and how many chickens does my uncle have?

### Karin From Algebra Class Says:

This is a very interesting problem!

This is a problem that can be solved using a system of equations.

In order to write a system of equations, you must have two variables, so ask yourself, what two things do I need to know?

You need to know how many dogs and how many chickens. So, we're going to let x= the number of dogs and y = the number of chickens.

Now we need to write two equations. We know information about two things: the number of legs and the number of heads.

Let's write an equation about the number of legs. How many legs does a dog have? 4. How many legs does a chicken have? 1.

4x + 2y = 148 (4 legs times number of dogs & 2 legs times number of chickens)

Now lets write an equation about the number of heads. How many heads does a dog have? 1. How many heads does a chicken have? 1.

x + y = 60. (Since each only has one head, we do not need to write the coefficient, 1).

Now you need to solve your the system of equations:
4x + 2y = 148
x + y = 60.

I would use the substitution method.

x + y = 60 can be rewritten as y = -x + 60

Substitute this into the first equation for y.

4x + 2(-x + 60) = 148

4x -2x + 120 = 148
2x + 120 = 148
2x +120 -120 = 148 - 120
2x = 28
2x/2 = 28/2
x = 14

Then substitute your value for x into the second equation and solve.

14 + y = 60

14 -14 + y = 60 - 14
y = 46

There were 14 dogs and 46 chickens.

Hope this helps.

Visit System of Equations for more help.

### Comments for Systems of Equations Help

Average Rating    May 23, 2011 Rating     WONDERFUL!!!!!!!!! by: Anonymous This was very helpful because i am in the 7th grade and in the advanced class and we are starting 8th grade work and this helped a whole lot Thank u to whom ever does this!

 Feb 02, 2011 Rating   Systems by: Anonymous To solve, I discovered a formula for this system. Ax+By=C Dx+Ey=F BF-BC x=–––––– DB-EA C-AX y=––––– B Example 2x+2y=14 x+3y=17 2•17-3•14 34-42 -8 x= ––––––––– = ––––– = –– = 2 1•2-2•3 2-6 -4 14-2•2 14-4 10 y= –––––– = –––– = –– = 5 2 2 2 The solution is (2,5), and to prove it 2•2+2≠5=14 4+10=14 14=14 2+3•5=17 2+15=17 17=17 Need More Help With Your Algebra Studies?