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# Polynomials
## Factorising
- **Infinitely many solutions** - lines are equal
- **No solution** - lines are parallel
-### Solving $\begin{cases}px + qy = a \\ rx + sy = b\end{cases}$ for one, infinite and no solutions
+### Solving $\protect\begin{cases}px + qy = a \\ rx + sy = b\protect\end{cases}$ for one, infinite and no solutions
where all coefficients are known except for one, and $a, b$ are known
Or use Matrix -> `det` on CAS.
-### Solving $\begin{cases}a_1 x + b_1 y + c_1 z = d_1 \\
+### Solving $\protect\begin{cases}a_1 x + b_1 y + c_1 z = d_1 \\
a_2 x + b_2 y + c_2 z = d_2 \\
-a_3 x + b_3 y + c_3 z = d_3\end{cases}$
+a_3 x + b_3 y + c_3 z = d_3\protect\end{cases}$
- Use elimination
- Generate two new equations with only two variables