Final answer:
To solve the given simultaneous equations, the method of substitution or elimination is used, resulting in the solution x = 1 and y = 3.
Step-by-step explanation:
To solve the simultaneous equations 2x + 3y = 11 and 3x + 5y = 18, we'll use the method of substitution or elimination. We'll solve the first equation for x:
x = (11 - 3y) / 2
Now, we substitute this x-value into the second equation:
3((11 - 3y) / 2) + 5y = 18
Multiplying through by 2 to clear the denominator, we get:
3(11 - 3y) + 10y = 36
This simplifies to:
33 - 9y + 10y = 36
Which then simplifies to y = 3. Next, we substitute y back into the first equation:
2x + 3(3) = 11
2x + 9 = 11
2x = 2
x = 1
The solution to the system of equations is x = 1 and y = 3.