Solve {l}{A_{1}x+B,y+c_{1}z+D_{1}}{Delta_{2}x+B_{2}y+C_{2}z+D_{2}}

$$\left\{ \begin{array} { l } { A _ { 1 } x + B , y + c _ { 1 } z + D _ { 1 } } \\ { \Delta _ { 2 } x + B _ { 2 } y + C _ { 2 } z + D _ { 2 } } \end{array} \right.$$

Least Common Multiple

$$\left(A_{1}x+B\right)\left(y+c_{1}z+D_{1}\right)\left(x\Delta _{2}+B_{2}y+C_{2}z+D_{2}\right)$$

Solution Steps

Identify all the factors and their highest power in all expressions. Multiply the highest powers of these factors to get the least common multiple.

$$\left(A_{1}x+B\right)\left(y+c_{1}z+D_{1}\right)\left(x\Delta _{2}+B_{2}y+C_{2}z+D_{2}\right)$$

Expand the expression.

$$A_{1}D_{1}\Delta _{2}x^{2}+A_{1}B_{2}xy^{2}+A_{1}B_{2}c_{1}xyz+A_{1}B_{2}D_{1}xy+A_{1}C_{2}xyz+A_{1}D_{1}D_{2}x+A_{1}D_{2}xy+Bxy\Delta _{2}+A_{1}C_{2}c_{1}xz^{2}+A_{1}C_{2}D_{1}xz+A_{1}D_{2}c_{1}xz+Bc_{1}xz\Delta _{2}+BD_{1}x\Delta _{2}+BB_{2}y^{2}+A_{1}y\Delta _{2}x^{2}+BB_{2}c_{1}yz+BB_{2}D_{1}y+BC_{2}yz+BD_{2}y+BC_{2}c_{1}z^{2}+A_{1}c_{1}z\Delta _{2}x^{2}+BC_{2}D_{1}z+BD_{2}c_{1}z+BD_{1}D_{2}$$

Evaluate

$$A_{1}x+B,\ y+c_{1}z+D_{1},\ x\Delta _{2}+B_{2}y+C_{2}z+D_{2}$$