Equating coefficients is the process of setting the coefficients of two like terms equal to each other in order to solve for a variable. This is often useful in algebraic equations and systems of equations.
For example, if given the equation 2x + 3y = 10 and asked to solve for x, you could rearrange the equation to isolate x:
2x + 3y = 10 2x = 10 - 3y
But what if you were given the equation 5x - 2y = 3x + 4y and asked to solve for x? Here is where equating coefficients comes in.
First, you need to simplify the equation by combining like terms:
5x - 2y = 3x + 4y 2x - 2y = 0
Now, you can equate the coefficients of x on each side of the equation:
2x = 0
This tells you that x must equal 0 in order for the equation to be true.
In summary, equating coefficients is a handy tool for solving equations that involve variables with similar terms.
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