Final answer:
To solve the given system of equations using Cramer's Rule, we first find the determinant D which is 32 then determine Dz and Dy which comes to 40 and 30 respectively. Finally, we use Cramer's Rule to find the values of x and y. The solution is x = 1.25 and y = 4.0625.
Step-by-step explanation:
To solve the system using Cramer's Rule, we need to find the determinant D first. D is the determinant of the coefficients of the variables x and y. Using the given system of equations:
3x - 5y = -22
4x - 4y = -16
The determinant D is calculated as follows:
D = (3 * -4) - (4 * -5) = 12 - (-20) = 12 + 20 = 32.
The determinant Dz can be found by replacing the coefficients of the variable z with the constants from the right side of each equation. So, Dz for the given system is:
Dz = (3 * -16) - (4 * -22) = -48 - (-88) = -48 + 88 = 40.
The determinant Dy can be found similarly, by replacing the coefficients of the variable y with the constants:
Dy = (3 * -(-22)) - (4 * -(-16)) = 3 * 22 - 4 * (-16) = 66 + 64 = 130.
Now, we can solve for x and y using Cramer's Rule:
x = Dz / D = 40 / 32 = 1.25
y = Dy / D = 130 / 32 = 4.0625