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To solve the system of equations:

2x + 3y = 10 …(1)

4x – y = 5 …(2)

We can use the method of substitution or elimination. Let’s use the method of substitution.

From equation (2), we can isolate y:

y = 4x – 5

Now, substitute this value of y into equation (1):

2x + 3(4x – 5) = 10

Simplify the equation:

2x + 12x – 15 = 10

14x – 15 = 10

Add 15 to both sides:

14x = 10 + 15

14x = 25

Divide both sides by 14:

x = 25/14

Now substitute this value of x back into equation (2) to find y:

4(25/14) – y = 5

Simplify the equation:

100/14 – y = 5

(100 – 14y)/14 = 5

Multiply both sides by 14:

100 – 14y = 70

Subtract 100 from both sides:

-14y = 70 – 100

-14y = -30

Divide both sides by -14:

y = -30/-14

y = 15/7

Therefore, the solution to the system of equations is:

x = 25/14

y = 15/7