What are x and y in the following system.2x+2y =5x-3y= -2

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justaguide eNotes educator | Certified Educator

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We have to find x and y given the equations 2x+2y=5 and x-3y= -2

x - 3y = -2

=> x = 3y - 2

substitute this in 2x + 2y = 5

=> 2*(3y - 2) + 2y = 5

=> 6y - 4 + 2y = 5

=> 8y = 9

=> y = 9/8

x = 3*(9/8) - 2

=> x = 11/ 8

Therefore we get x = 11/8 and y = 9/8

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hala718 eNotes educator | Certified Educator

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2x+ 2y = 5...........(1)

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

We will use the substitution method to solve.

From (2) we will re write x= 3y-2

Now we will substitute into (1).

==> 2x +2y = 5

==> 2(3y-2) + 2y = 5

==> 6y - 4 + 2y = 5

==> 8y = 9

==> y= 9/8

==> x = 3y-2 = 3(9/8) -2 = (27- 16)/8 = 11/8

Then the answer is the pair ( 11/8 , 9/8).

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