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Get ready to unleash your problem-solving skills as we dive into the world of simultaneous equations. Join us as we demystify the elimination method, a powerful technique to find the solutions to a system of equations. Through captivating examples and step-by-step explanations, we'll guide you on how to eliminate one variable by adding or subtracting equations, ultimately leading to the solution. Witness the magic unfold as equations transform and solutions emerge.

Example: Solve the system of equations using the elimination method:

Equation 1: 2x + 3y = 7
Equation 2: 4x - 2y = 10

Solution:
To solve this system of equations, we'll eliminate one variable by adding or subtracting the equations.

Step 1: Multiply Equation 1 by 2 to make the coefficient of x in both equations equal:

Equation 1 (multiplied by 2): 4x + 6y = 14
Equation 2: 4x - 2y = 10

Step 2: Subtract Equation 2 from Equation 1:

(4x + 6y) - (4x - 2y) = 14 - 10
4x + 6y - 4x + 2y = 4
8y = 4

Step 3: Solve for y:

8y = 4
y = 4/8
y = 1/2

Step 4: Substitute the value of y back into either equation to solve for x. Let's use Equation 1:

2x + 3y = 7
2x + 3(1/2) = 7
2x + 3/2 = 7
2x = 7 - 3/2
2x = 11/2
x = (11/2) / 2
x = 11/4

Step 5: The solution to the system of equations is x = 11/4 and y = 1/2.

Therefore, the simultaneous equations 2x + 3y = 7 and 4x - 2y = 10 are solved using the elimination method, resulting in x = 11/4 and y = 1/2.