Question

Find the solution of this system of linear equations:
10x = -65 - 5y
-5x = 40 - 5y

Answer 1

To solve the system of linear equations, we use the elimination method to first find x, which is -5, then substitute it back to find y, which is 3. The solution to the system is x = -5 and y = 3.

Step-by-step explanation:

The question asks to find the solution of a system of linear equations. The system given is:

• 10x = -65 - 5y
• -5x = 40 - 5y

To solve these simultaneous equations, you can use either substitution or elimination methods. Since both equations contain -5y, elimination seems efficient. First, align the equations:

1. 10x + 5y = -65
2. -5x + 5y = 40

By adding equation (1) and (2), we can eliminate y:

1. (10x + 5y) + (-5x + 5y) = -65 + 40
2. (10x - 5x) + (5y + 5y) = -25
3. 5x = -25
4. x = -5

Now, substitute x = -5 into either equation (1) or (2) to find y. Let's use equation (2):

1. -5(-5) + 5y = 40
2. 25 + 5y = 40
3. 5y = 15
4. y = 3

Thus, the solution to the system is x = -5 and y = 3.