Question

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

Answer 1

Answer: x = 4 , y = -3

Step-by-step 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