Solve {l}{a=2i+3j}{b=-3i+4j}{c=ma+nb}{o=m}{text{Solvefor}ptext{where}}{p=o}

$$\left. \begin{array} { l } { a = 2 i + 3 j }\\ { b = -3 i + 4 j }\\ { c = m a + n b }\\ { o = m }\\ { \text{Solve for } p \text{ where} } \\ { p = o } \end{array} \right.$$

Solve for a, j, b, c, m, n, o, p

$$a=\frac{17in+3c}{3m+4n}\text{, }j=\frac{c+3in-2im}{3m+4n}\text{, }b=\frac{4c-17im}{3m+4n}\text{, }c\in \mathrm{C}\text{, }m\in \mathrm{C}\setminus -\frac{4n}{3},0\text{, }n\in \mathrm{C}\text{, }o=m\text{, }p=m$$

$$a=-\frac{bn-c}{m}\text{, }j=\frac{c-bn-2im}{3m}\text{, }b\in \mathrm{C}\text{, }c\in \mathrm{C}\text{, }m\neq 0\text{, }n\in \mathrm{C}\text{, }o=m\text{, }p=m$$

$$a=\frac{17in+3c}{4n}\text{, }j=\frac{3in+c}{4n}\text{, }b=\frac{c}{n}\text{, }c\in \mathrm{C}\text{, }m=0\text{, }n\neq 0\text{, }o=0\text{, }p=0$$

$$a=\frac{3b+17i}{4}\text{, }j=\frac{b+3i}{4}\text{, }b\in \mathrm{C}\text{, }c=0\text{, }m=0\text{, }n=0\text{, }o=0\text{, }p=0$$