Question

Solve the following simultaneous equations by first multiplyin

one equation by a constant to give an equivalent equation:
5x + 2y = 54
2x - y = 9

Answer 1

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.