Final answer:
To solve the simultaneous equations 5x + 2y = 54 and 2x - y = 9, we first multiply the second equation by 2 to make the coefficients of y in both equations the same. Then we add the two equations together to eliminate y and solve for x. Finally, we substitute the value of x into one of the original equations to solve for y.
Step-by-step explanation:
To solve the simultaneous equations 5x + 2y = 54 and 2x - y = 9, we'll first multiply the second equation by 2 to make the coefficients of y in both equations the same:
2(2x - y) = 2(9) → 4x - 2y = 18
Now we have two equivalent equations:
5x + 2y = 54
4x - 2y = 18
We can solve this system of equations by adding the two equations together:
(5x + 4x) + (2y - 2y) = 54 + 18 → 9x
= 72
Dividing both sides by 9 gives us x = 8. Now we substitute this value of x into one of the original equations to solve for y:
5(8) + 2y = 54 → 40 + 2y
= 54 → 2y
= 14 → y
= 7
Therefore, the solution to the simultaneous equations is x = 8 and y = 7.