1. Problem: Convert the simultaneous linear equations into matrix form. 2. The matrix form of simultaneous linear equations $ax + by = c$ and $dx + ey = f$ is: $$\begin{bmatrix} a & b \\ d & e \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} c \\ f \end{bmatrix}$$ 3. For each part, identify coefficients of $x$ and $y$ and constants on the right side. 4. (a) Equations: $x - y = 7$, $x + 3y = 5$ Matrix form: $$\begin{bmatrix} 1 & -1 \\ 1 & 3 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 7 \\ 5 \end{bmatrix}$$ 5. (b) Equations: $3x + y = 0$, $5x + 2y = -14$ Matrix form: $$\begin{bmatrix} 3 & 1 \\ 5 & 2 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 0 \\ -14 \end{bmatrix}$$ 6. (c) Equations: $7x + 2y = -11$, $2x - y = -10$ Matrix form: $$\begin{bmatrix} 7 & 2 \\ 2 & -1 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} -11 \\ -10 \end{bmatrix}$$ 7. (d) Equations: $3x + 2y = 14$, $-5x + 4y = 5$ (rewritten $4y - 5x = 5$) Matrix form: $$\begin{bmatrix} 3 & 2 \\ -5 & 4 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 14 \\ 5 \end{bmatrix}$$ 8. (e) Equations: $2x + y = -4$ (rewritten $2x + y + 4 = 0$), $-3x + y = 11$ (rewritten $y - 3x = 11$) Matrix form: $$\begin{bmatrix} 2 & 1 \\ -3 & 1 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} -4 \\ 11 \end{bmatrix}$$ 9. (f) Equations: $2x + y = -9$, $5x = -12$ (rewritten $5x + 0y = -12$) Matrix form: $$\begin{bmatrix} 2 & 1 \\ 5 & 0 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} -9 \\ -12 \end{bmatrix}$$ 10. (g) Equations: $2x = 5y$ (rewritten $2x - 5y = 0$), $\frac{5}{3}x + 2y = 3$ Matrix form: $$\begin{bmatrix} 2 & -5 \\ \frac{5}{3} & 2 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 0 \\ 3 \end{bmatrix}$$ 11. (h) Equations: $\frac{x}{y} = 4$ (rewritten $x - 4y = 0$), $0.8(x + 5) = 3y$ (rewritten $0.8x + 4 = 3y$ or $0.8x - 3y = -4$) Matrix form: $$\begin{bmatrix} 1 & -4 \\ 0.8 & -3 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 0 \\ -4 \end{bmatrix}$$ Final answers are the matrix forms above for each part (a) to (h).