When it comes to solving systems of equations, one of the most commonly used methods is substitution. This method involves solving one equation for one variable and then substituting that expression into the other equation. This allows you to eliminate one variable and solve for the other, ultimately finding the solution to the system of equations.
Substitution is a straightforward and efficient method for solving systems of equations, making it a popular choice for many students and professionals alike. By following a few simple steps and carefully substituting variables, you can easily find the solution to even complex systems of equations.
Steps to Solve System of Equations by Substitution:
1. Begin by solving one of the equations for one of the variables. Choose the equation that is easiest to solve for one variable. For example, if you have the equations:
2x + 3y = 7
4x – y = 5
You can solve the second equation for y: y = 4x – 5.
2. Substitute the expression you found in step 1 into the other equation. Using the example above, substitute y = 4x – 5 into the first equation: 2x + 3(4x – 5) = 7.
3. Solve the resulting equation for the remaining variable. In the example above, solve for x: 2x + 12x – 15 = 7, which simplifies to 14x – 15 = 7. So, 14x = 22, and x = 22/14 = 11/7.
4. Substitute the value of x back into one of the original equations to solve for the other variable. Using the example above, substitute x = 11/7 into the second equation: 4(11/7) – y = 5. Solve for y to get y = 13/7.
5. Check your solution by substituting the values of x and y into both original equations to ensure they satisfy both equations.
By following these steps, you can easily solve systems of equations using the substitution method. Practice with a variety of problems to strengthen your skills and become more comfortable with this method.
In conclusion, solving systems of equations by substitution is a valuable skill that can be used in various mathematical and real-world scenarios. By mastering this method and practicing regularly, you can confidently tackle complex systems of equations and find accurate solutions efficiently.