1. Solving Linear Systems of Equations - Substitution Method Recall that to solve the linear system of equations in two variables... we need to find the value of x and y that satisfies both equations. In this presentation the Substitution Method will be demonstrated. Example 1: Solve the following system of equations...

2. Label the equations as # 1 and # 2. Start with equation # 2 and solve for x... Since y - 2 is the same value as x, we can substitute y - 2 for x in equation # 1...

3. Solve this equation for y... Substitute this value for y in equation # 2 and solve for x... The solution to the system is (1,3).

4. Summary: 1) Solve for one variable in either equation. Choose a variable that has a coefficient of 1 or -1 if possible (to avoid fractions). 2) Substitute the expression for the variable in the other equation. This leaves one equation in one unkown, for which we can solve. 3) Substitute the given value for the variable into either equation and solve for the other variable.

5. Example 2: Solve the following system of equations... Solve the second equation for y...

6. Substitute the expression for y in equation # 1... and solve for x...

7. Substitute the value for x into equation # 1 (either equation could be used at this point)... and solve for y... The solution to the system is...

8. Since equation # 1 was used in the last step, check by substituting the values into equation # 2...