Calculate the solution to these simultaneous equations using the elimination method: (1)(1)2𝑥+𝑦2x+y==00 (2)(2)𝑥−𝑦x−y==66

Sure, let's solve these simultaneous equations step by step:

1. The given equations are: 2x + y = 0 ...(Equation 1) x - y = 6 ...(Equation 2)

2. To use the elimination method, we need to make the coefficients of y the same in both equations. We can do this by multiplying Equation 2 by 2:

   2x + y = 0 ...(Equation 1) 2x - 2y = 12 ...(Equation 2)

3. Now, we subtract Equation 2 from Equation 1:

   (2x + y) - (2x - 2y) = 0 - 12 This simplifies to: 3y = -12

4. To find the value of y, we divide both sides of the equation by 3:

   y = -12 / 3 y = -4

5. Now that we have the value of y, we can substitute it into Equation 1 to find the value of x:

   2x + (-4) = 0 2x = 4 x = 4 / 2 x = 2

So, the solution to the simultaneous equations is x = 2 and y = -4.