In this post, we will explore the substitution method for solving systems of linear equations. This approach involves solving one equation for a variable and then substituting that expression into the other equation. Let's consider an example:

Example 1:

Consider the system of equations:

2x + y = 7
3x - 2y = 4

First, we solve the first equation for x:

x = (7 - y)/2

Next, we substitute this value of x into the second equation:

3(7 - y)/2 - 2y = 4

Simplifying the equation, we get:

21 - 3y - 4y = 8

Combining like terms, we have:

-7y = -13

Finally, dividing both sides by -7, we find:

y = 13/7

Substituting this value back into the first equation, we can solve for x:

x = (7 - 13/7)/2

Simplifying the equation further, we obtain:

x = 6/7

Therefore, the solution to the system of equations is x = 6/7 and y = 13/7.

Pros and Cons of the Substitution Method:

The substitution method is useful when one of the equations is already solved for a variable, making it easier to substitute into the other equation. However, it can become tedious and time-consuming when dealing with more complex systems or equations with multiple variables.

Conclusion

The substitution method provides an effective way to solve systems of linear equations. By substituting one equation into another, we can find the values of the variables that satisfy both equations. Remember to always check your solutions by substituting them back into the original equations!

Keep practicing, and soon the substitution method will become second nature to you!