2. Solving Linear Systems Substitution Method Lisa Biesinger Coronado High School Henderson,Nevada

3. Linear Systems A linear system consists of two or more linear equations. The solution(s) to a linear system is the ordered pair(s) (x,y) that satisfy both equations.

4. Example Linear System: The solution will be the values for x and y that make both equations true.

5. Solving the System Step 1: Solve one of the equations for either x or y. For this system, the first equation is easy to solve for x because the coefficient of x is equal to 1.

6. Organizing Your Work Set up 2 columns on your paper. Place one equation in each column. Write the equation we are using first in column 1, and the other equation in column 2.

7. Solving by Substitution Now we will solve for x in column 1.

8. Solving by Substitution Subtract 2y from both sides.

9. Solving the System Step 2: Substitute your answer into the other equation in column 2. Substituting will eliminate one of the variables in the equation.

10. Solving by Substitution Always use parenthesis when substituting an expression with two terms.

11. Solving the System Step 3: Simplify the equation in column 2 and solve.

12. Solving by Substitution Use the distributive property and combine like terms.

13. Solving by Substitution Solve for y.

14. Solving the System Step 4: Substitute your answer in column 2 into the equation in column 1 to find the value of the other variable.

15. Solving by Substitution Substitute for y and solve for x. Solve for x.

16. The Solution The solution to this linear system is and. The solution can also be written as an ordered pair

17. Almost Finished Checking Your Solution Check your answer by substituting for x and y in both equations.

18. Checking Your Answer  

19. Additional Examples Problem #1: Problem#2 Problem #3 Answers: #1 #2 #3