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