Find the numerical lengths of the diagonals of the parallelogram below where FB=4x-2 FD=3y-1 FC=3x and FA=3y-3. solve using a system of equations via substitution or elimination methods.

BD = 28

AC = 24

Step-by-step explanation:

Diagonals of a parallelogram bisect each other.

4x − 2 = 3y − 1

3x = 3y − 3

Using elimination to solve the system of equations, subtract the second equation from the first.

(4x − 2) − 3x = (3y − 1) − (3y − 3)

4x − 2 − 3x = 3y − 1 − 3y + 3

x − 2 = 2

x = 4

Substitute into either equation to find y.

3(4) = 3y − 3

12 = 3y − 3

15 = 3y

y = 5

The length of BD is:

4(4) − 2 + 3(5) − 1 = 28

The length of AC is:

3(4) + 3(5) − 3 = 24

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