5.1 System of Equation - Substitution

The substitution method is a method for solving a system of equations. It involves the following steps:

1. Solve one equation for one of the variables.

2. Substitute the expression you found in step 1 into the other equation.

3. Solve the resulting equation for the remaining variable.

4. Substitute the value you found in step 3 into the equation you solved in step 1 to find the value of the other variable.

Here is an example of how to solve a system of equations using the substitution method:

• Equation 1: 2x + 3y = 12

• Equation 2: x - y = 4
  

First, we solve Equation 1 for x:

x = (12 - 3y) / 2

Now, we substitute this expression into Equation 2:

(12 - 3y) / 2 - y = 4

Simplifying, we get:

-5y = 4

y = -0.8

Now that we know the value of y, we can substitute it into Equation 1 to find the value of x:

2x + 3(-0.8) = 12 2x = 16 x = 8

Therefore, the solution to the system of equations is x = 8 and y = -0.8.

Here are some additional tips for using the substitution method:

• If one of the equations is already solved for one of the variables, you can skip step 1.

• If both equations are already solved for one of the variables, you can simply set the two expressions equal to each other and solve for the remaining variable.

• If the system of equations has no solution, the substitution method will not work. In this case, you can try using the elimination method or the graphical method to solve the system.