Solving System of Linear Equations: (lesson 1 of 5)
Substitution Method
The substitution method is most useful for systems of 2 equations in 2 unknowns.
The main idea here is that we solve one of the equations for one of the
unknowns, and then substitute the result into the other equation.
Substitution method can be applied in four stepsThe main idea here is that we solve one of the equations for one of the
unknowns, and then substitute the result into the other equation.
Step 1:
Solve one of the equations for either x = or y = .
Step 2:Substitute the solution from step 1 into the other equation.
Step 3:Solve this new equation.
Step 4:Solve for the second variable.
Example 1: Solve the following system by substitution
Solution:
Step 1: Solve one of the equations for either x = or y = . We will solve second equation for y.
Note: It does not matter which equation we choose
first and which second. Just choose the most convenient one first!
first and which second. Just choose the most convenient one first!
Example 2: Solve by substitution
Solution:
Step 1: Solve one of the equations for either x = or y =. Since the coefficient of y in equation 2 is -1, it is easiest to solve for y in equation 2.
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