If 8 pens and 4 pencil costs $9.36 and 4 pencil and 8 eraser costs # $10.08.. what is the cost of each pen, pencil and eraser?
8x + 4y = 9.36 and 4y + 8z = 10.08. I can see that z is .08 times of x but I am not sure how to derive the value of x y and z. I appreciate your help and thoughts on this.
Are you sure there is not more to the problem? The general solution to problems where there are more unknowns (the x, y, and z in this case) than equations (two in this case) contains ideas like singular value decomposition, null spaces and pseudo inverses. That seems a little more than Beginning Algebra.
Edit:
Anyway, without anymore information, pick any one of the x, y, or z and assume that is a 'known value'. Then re-write the equations so that you have two unknowns and two equations and solve for the unknown values in terms of the known values, i.e. you would have two functions. For example if you chose y as the unknown you would have
x = 1.17 - 0.50 y
z = 1.26 - 0.50 y
If we let y=\(\displaystyle \alpha\). we could write
x = 1.17 - 0.50 \(\displaystyle \alpha\)
y = \(\displaystyle \alpha\)
z = 1.26 - 0.50 \(\displaystyle \alpha\)
and the null space of the matrix associated with the coefficient matrix (written in a particular order) would be (-0.5, 1, -0.5), i.e. the three coefficients for alpha.
BTW: If x were chosen as the know value, z would be a constant plus x, not .08 times x.
