Question

Find the unique solution to the following system of equations, if possible, using Cramer's rule.

(a) x + y = 34
(b) 2x - 3y = 5

Answer 1

To solve the system of equations using Cramer's rule, find the determinants of the coefficient matrix and the matrix formed by replacing the column of coefficients with the constants. Then, calculate the solution using the determinants.

Step-by-step explanation:

To solve the system of equations using Cramer's rule, we need to find the determinants of the coefficient matrix and the determinant of the matrix formed by replacing the column of coefficients with the constants. Let's call the determinants D, Dx, and Dy.

First, calculate D. D = (1 * (-3)) - (2 * 1) = -5.

Then, calculate Dx. Dx = (34 * (-3)) - (2 * 1) = -112.

Finally, calculate Dy. Dy = (1 * 5) - (2 * 34) = -63.

The solution is given by x = Dx / D = -112 / -5 = 22.4 and y = Dy / D = -63 / -5 = 12.6.