Solve the system of equations using Cramer's rule: 1) x-4y=-10 2) 2x+3y=2

Step 1: Solve Question 1.i.
The given system of equations is:

1. $x-4y=-10$
2. $2x+3y=2$

We use Cramer's rule. First, calculate the determinant of the coefficient matrix, $D$:

$$D = \begin{vmatrix} 1 & -4 \\ 2 & 3 \end{vmatrix} = (1)(3) - (-4)(2) = 3 - (-8) = 3+8 = 11$$

Next, calculate the determinant $D_x$ by replacing the first column of $D$ with the constant terms:

$$$$