How do you cancel out a variable with an x For an algebraic equation

Answer 1

As long as you have at least n expressions that involve no more than n variables, you can solve the system of expressions in one of several ways.

Factoring - if the expression is a quadratic of the general form ax²+bx+c=0, it may be possible to factor that equation into something like (rx+y)(sx+z)=0, which should yield two, one or no real values for x.

Substitution - rearrange one equation so that one variable is in terms of the other(s) and substitute that value for the variable on another expression. Repeat as needed, eliminating one variable each time until you are down to just one, which you them any be able to determine a value for. Then work backwards to determine values for the other(s). For example, for x+y=a and 3x+2y=b, you can rearrange the first to x=a-y and then substitute into the second as 3(a-y)+2y=b and then solve for y, which you can then use to derive x.

Subtraction - If you can multiply one expression so that one of its variables has the same coefficient as the other, you can then subtract it from the other. For example, with the two expressions above, you could multiply the first by 2 to get 2x+2y=2a. Then subtracting from the 2nd leaves x=b-2a