Solve the system:   x+2y = 5    2x-3y = 2

Expert Answers

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If x + 2y = 5, then we can find a value for x by subtracting 2y from both sides.  That value is

x = 5 - 2y

Now substitute that in to the second equation.

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

Once we do the math on that, we get

10 - 4y - 3y = 2

10 - 7y = 2

Now we subtract 10 from both sides and we get

-7y = - 8

Divide both sides by -7 and we have

y = 8/7

If y = 8/7

x + 2(8/7) = 5

x + 16/7 = 5

x = 5 - 16/7

x = 35/7 - 16/7

x = 19/7

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

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

Using the elimination method:

Multiply (2) by -2 and add to (1)

-7 y = -8

==> y= 8/7

Now substitute:

x + 2y = 5

x = 5 - 2y

    = 5 - 2(8/7)

      = 5- 16/7

      = (35-16)/7

      = 19/7

x = 19/7

Approved by eNotes Editorial Team
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