Question

Solve the simultaneous equations 2x + 3y = -2 and 2x + 5y = 2. What are the solutions?

Options:
A) x = 2, y = -4
B) x = 4, y = -2
C) x = -2, y = 4
D) x = -4, y = 2

Answer 1

To solve the simultaneous equations, we used the elimination method, subtracting the second equation from the first to eliminate x, then solving for y, and back-substituting to find x. The solutions are x = -4 and y = 2, corresponding to option D.

Step-by-step explanation:

To solve the simultaneous equations 2x + 3y = -2 and 2x + 5y = 2, we can use the substitution or elimination method. In this case, the elimination method is more straightforward. Here's how to do it step-by-step:

1. First, we write down both equations:

• 2x + 3y = -2
• 2x + 5y = 2

Next, we subtract the second equation from the first to eliminate the x-term:

• (2x + 3y) - (2x + 5y) = -2 - 2
• The 2x terms cancel out, leaving us with -2y = -4

Divide both sides by -2 to solve for y:

• y = 2

Now we can substitute y back into one of the original equations to solve for x. We'll use the first equation:

• 2x + 3·2 = -2
• 2x + 6 = -2
• 2x = -8
• x = -4

Therefore, the solutions are x = -4 and y = 2, which corresponds to option D.