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Use Cramer's Rule to find x in the system of equations below.

2x − 3y = 17

5x + 4y = 8

1 Answer

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Answer: x = 4 , y = -3

Explanation:

Going by the Cramer's rule , we first determine the determinant by dealing with only the coefficients of x and y in the 2 x 2 matrix.

2x - 3y = 17

5x + 4y = 8

2 -3

5 4, going by the rule now, we now have

(2 x 4) - (5 x -3)

8 + 15

= 23.

Now to find the value of x , replace the constants with the coefficient of x and divide by he determinants.

17 -3

8 4

---------------

2 -3

5 4

( 17 x 4 ) - ( 8 x -3 )

---------------------------

23

= 68 + 24

------------

23

= 92/23

= 4.

x = 4

Now to find y, just repeat the process by replacing the coefficient of y with the constants.

2 17

5 8

-----------

2 -3

5 4

( 2 x 8 ) - ( 5 x 17 )

-----------------------

23

16 - 85

---------

23

= -69/23

= -3

y = -3.

check

substitute for the values in any of the equations above.

2(4) - 3(-3)

8 + 9

= 17

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