how to do the elimination method for solving math algebraic problems

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Welcome to learning the elimination method! This is one of the most effective techniques for solving systems of linear equations. The elimination method works by strategically adding or subtracting equations to eliminate one variable, making the system easier to solve. Let's look at a simple example system with two equations and two unknowns. The elimination method follows a systematic nine-step process. First, we write both equations in standard form. Then we choose which variable to eliminate - usually the one with simpler coefficients. Next, we make the coefficients of that variable either opposites or equal by multiplying equations. We then add or subtract to eliminate the variable, solve for the remaining one, substitute back, and find our solution. Now let's work through a complete example. We have the system: two x plus three y equals seven, and x minus y equals one. First, we choose to eliminate y since it has simpler coefficients. We multiply the second equation by three to get three x minus three y equals three. Then we add both equations together, and the y terms cancel out, giving us five x equals ten. Solving for x, we get x equals two.