Question

Using Cramer's Rule, what is the value of the y-coordinate for the system of equations:

x+3y=−3
4x+4y=17
a. -4
b. 3
c. 5
d. 7

Answer 1

To find the y-coordinate for the given system of equations using Cramer's Rule, we first calculate the determinant of the coefficient matrix. Then, we find the determinant when the column for the y-coefficients is replaced with the constants. Finally, we divide the determinant of the y-column by the determinant of the coefficient matrix to get the value of y. None of the options are correct.The value of the y-coordinate is -21.

Step-by-step explanation:

To find the value of the y-coordinate using Cramer's Rule for the system of equations:

x+3y=-3

4x+4y=17

First, we find the determinant of the coefficient matrix, D:

D = |1 3| = 1*4 - 3*1 = 1

Next, we replace the column for the y-coefficients with the constants and find the determinant, Dx:

Dx = |-3 3| = -3*4 - 3*(-3) = -21

Finally, we calculate the value of y using Cramer's Rule:

y = Dx / D = -21 / 1 = -21

Therefore, the value of the y-coordinate is -21.