1. The problem is to write formulas for linear systems, which are sets of linear equations with multiple variables. 2. A linear system can be written as: $$\begin{cases} a_1x + b_1y = c_1 \\ a_2x + b_2y = c_2 \end{cases}$$ where $a_1, b_1, c_1, a_2, b_2, c_2$ are constants and $x, y$ are variables. 3. Important rules: - Each equation represents a line in the coordinate plane. - The solution to the system is the point(s) where the lines intersect. - Systems can have one solution (intersecting lines), no solution (parallel lines), or infinitely many solutions (same line). 4. To solve, you can use substitution, elimination, or graphing methods. 5. Example of substitution formula: From the first equation, solve for $x$: $$x = \frac{c_1 - b_1y}{a_1}$$ Substitute into the second equation: $$a_2\left(\frac{c_1 - b_1y}{a_1}\right) + b_2y = c_2$$ 6. Example of elimination formula: Multiply equations to align coefficients and add or subtract to eliminate a variable: $$m \times (a_1x + b_1y = c_1)$$ $$n \times (a_2x + b_2y = c_2)$$ Then add or subtract to eliminate $x$ or $y$. 7. These formulas help solve linear systems efficiently in grade 10 algebra.