In solving systems of equations, the substitution method provides a systematic approach to find the values of variables without the need for graphing. This method is particularly useful when equations are complex or when graphing is impractical. The goal is to express one variable in terms of the other and substitute it into the second equation, simplifying the problem.

To begin, identify the easier equation to isolate a variable, which we will label as equation A. For instance, if you have the equation y = 7x - 14, it is already solved for y. The second equation will be labeled as equation B. The next step involves substituting the expression from equation A into equation B. This means wherever y appears in equation B, you replace it with 7x - 14.

After substitution, the equation will typically reduce to a single variable equation. For example, if equation B is 2x - y = 4, substituting gives 2x - (7x - 14) = 4. Simplifying this leads to -5x + 14 = 4, which can be solved to find x. In this case, solving yields x = 2.

Once you have the value of x, the next step is to substitute it back into either equation A or B to find the corresponding y value. Using equation A, substituting x = 2 gives y = 7(2) - 14, resulting in y = 0.

Finally, it is essential to verify the solution by substituting both values back into the original equations. For equation A, substituting x = 2 and y = 0 confirms the equation holds true. Similarly, checking equation B will also validate the solution. Thus, the solution to the system of equations is (x, y) = (2, 0).

This method not only streamlines the process of solving systems of equations but also reinforces the understanding of variable relationships and algebraic manipulation.