# solve the system:   x-2y = 5     2x-y = 3 solve the system:   x-2y = 5     2x-y = 3

## Expert Answers You may also consider the alternative method, that uses determinants, such that:

x-2y = 5

2x-y = 3

Form the determinant of the system such that: =  You need to find the variable x such that:    You need to find the variable y such that:    Hence, evaluating the solutions to the system yields and .

Approved by eNotes Editorial Team x-2y = 5 .........(1)

2x - y = 3 .........(2)

To solve the system , we will use the elimination method:

multiply (1) by -2 and add to (2);

==>-2x + 4y = -10

==> 2x - y  = 3

==> 3y = -7

==> y= -7/3

==> x = 2y + 5

= 2(-7/3) + 5 = -14/3 + 15/3 = 1/3

==> x = 1/3

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