# Thread: Changing this simultaneous equation into matrix form

1. Changing this simultaneous equation into matrix form

I have got two equations that I need help in changing to matrix format.

a=(b/(cX))+(b/(dY)) --- (1)
e=(b/(fX))+(b/(gY)) --- (2)

I know that the format for simultaneous equation to be solved by matrix got to be in the form of:

ax+by=c
dx+ey=f

only X and Y are unknown. The rest are all just constant. thanks again.

2. The problem appears to be that those are not linear equations and so cannot be written as a matrix equation.

3. Hello, chenxianghao!

Change this simultaneous equation into matrix form

. . $\displaystyle \begin{array}{cccc}\dfrac{b}{cx} +\dfrac{b}{dy}&=& a & (1) \\ \\[-3mm] \dfrac{b}{fx}+\dfrac {b}{gy} &=& e & (2) \end{array}$

$\displaystyle \begin{array}{ccccc}\text{Multiply [1] by }cd\!: & bd\,\dfrac{1}{x} + bc\,\dfrac{1}{y} &=& acd \\ \\[-3mm] \text{Multiply [2] by }fg\!: & bg\,\dfrac{1}{x} + bf\,\dfrac{1}{y} &=& e\!f\!g \end{array}$

$\displaystyle \text{Let: }\:X = \frac{1}{x},\;\;Y = \frac{1}{y}$

$\displaystyle \text{Then we have: }\;\;\begin{array}{ccc}bdX + bcY &=& acd \\ bgX + b\!fY &=& e\!fg \end{array}$

. . solve for $\displaystyle X\text{ and }Y$
. . then solve for $\displaystyle x\text{ and }y.$