When it comes to solving systems of equations, substitution is a commonly used method that can help simplify the process. By substituting one equation into another, we can eliminate one variable and solve for the remaining variable. This can be particularly useful when dealing with complex systems of equations that are difficult to solve using other methods.
In this worksheet, we will practice solving systems of equations by substitution. By following a step-by-step approach, you will learn how to apply this method effectively and confidently tackle any system of equations that comes your way.
Step 1: Choose one equation to solve for a variable
The first step in solving a system of equations by substitution is to choose one of the equations and solve for one of the variables. Let’s say we have the following system of equations:
3x + 2y = 8
2x – y = 4
We can choose the second equation and solve for y:
y = 2x – 4
Step 2: Substitute the expression into the other equation
Next, we substitute the expression we found for y into the other equation. In this case, we substitute y = 2x – 4 into the first equation:
3x + 2(2x – 4) = 8
3x + 4x – 8 = 8
7x – 8 = 8
Step 3: Solve for the remaining variable
Now that we have an equation with only one variable, we can solve for x:
7x – 8 = 8
7x = 16
x = 16/7
Once we have found the value of x, we can substitute it back into one of the original equations to solve for the other variable. In this case, we can use the second equation:
2(16/7) – y = 4
32/7 – y = 4
y = 32/7 – 4
y = -4/7
Step 4: Check your solution
It is important to always check your solution by substituting the values of x and y back into both equations to ensure that they satisfy both equations simultaneously. If they do, then you have successfully solved the system of equations by substitution.
By following these steps and practicing with different systems of equations, you will become more comfortable and confident in solving systems of equations by substitution. This method can be a powerful tool in your mathematical toolkit and can help you tackle even the most challenging systems of equations with ease.
With practice and perseverance, you will master the art of solving systems of equations by substitution and be well-equipped to handle any mathematical problem that comes your way.