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

Given:

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

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

Multiplying equation (1) by 2:

2x + 4y = 10 ... (3)

Subtracting equation (2) from (3):

2x - 2x + 4y + 3y = 10 - 2

==> 7y = 8

==> y = 8/7

Substituting this value of y in equation (1)

x + 2*(8/7) = 5

==> x + 16/7 = 5

==> x = 5 - 16/7 = 19/7

Answer:

x = 19/7, y = 8/7

The set of equations x+2y = 5 and 2x-3y = 2 has to be solved for x and y.

From x + 2y = 5, we get x = 5 - 2y

Substitute this in the second equation 2x - 3y = 2

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

10 - 4y - 3y = 2

10 - 7y = 2

-7y = -8

y = 8/7

Substitute this in x = 5 - 2y

x = 5 - 2*(8/7)

x = 5 - 16/7

x = (35 - 16)/7 = 19/7

The solution of the set of equations x+2y = 5 and 2x-3y = 2 is x = 19/7 and y = 8/7