Calculate the solution to these simultaneous equations using the elimination method: (1)(1)2𝑞−2𝑝2q−2p==1010 (2)(2)2𝑞+𝑝2q+p==11

The equations you provided seem to be formatted incorrectly, but I'll assume you meant:

1. 2q - 2p = 10
2. 2q + p = 11

Here's how you can solve these equations using the elimination method:

Step 1: Arrange the equations so that like terms are vertically aligned:

2q - 2p = 10 2q + p = 11

Step 2: Add the two equations together to eliminate one of the variables:

(2q - 2p) + (2q + p) = 10 + 11 4q - p = 21

Step 3: Solve for the remaining variable:

p = 4q - 21

Step 4: Substitute p into one of the original equations:

2q + (4q - 21) = 11 6q - 21 = 11 6q = 32 q = 32 / 6 q = 16/3

Step 5: Substitute q = 16/3 into the equation p = 4q - 21 to find p:

p = 4*(16/3) - 21 p = 64/3 - 63/3 p = 1/3

So, the solution to the system of equations is q = 16/3 and p = 1/3.