substitutionsmetoden

The substitution method is a technique used in algebra to solve systems of equations. It involves solving one of the equations for one variable and then substituting that expression into the other equation. This reduces the system of two equations with two variables into a single equation with one variable, which can then be solved.

To apply the substitution method, first choose one of the equations and isolate one of the variables. This means rearranging the equation so that one variable is by itself on one side. For example, if you have the equation 2x + y = 5, you could solve for y to get y = 5 - 2x.

Once one variable is expressed in terms of the other, substitute this expression into the *other* equation. If you solved for y in the first equation, you would replace every instance of y in the second equation with the expression you found. This new equation will only contain one variable, allowing you to solve for its value.

After finding the value of one variable, substitute this value back into either of the original equations (or the rearranged equation) to find the value of the other variable. This will give you the solution to the system of equations, which is an ordered pair (x, y) that satisfies both equations simultaneously.

The substitution method is particularly useful when one of the variables in one of the equations has a coefficient of 1 or -1, making it easy to isolate.