How do you solve systems of linear equations using the substitution or elimination method?

Linear equations often appear in various fields such as engineering, science, economics, and social sciences. The solution of these problems involves finding the values of variables that satisfy all given equations.

The two methods of solving systems of linear equations are substitution and elimination. In the substitution method, we solve one equation for one variable and substitute it into the other equation. This method produces an equation in one variable that we can easily solve.

In the elimination method, we add or subtract equations to eliminate one variable and solve for the other. We continue the process until we find the values of all variables.

Both methods involve algebraic manipulations of the given equations, and their effectiveness depends on the complexity of the equations.

To solve a system of linear equations, first, we need to write them in standard form (Ax + By = C). Then, apply one of the methods (substitution or elimination) to find the values of variables.

If the equations are in non-standard form, we can rearrange them to the standard form by performing algebraic manipulations.