Tuesday, October 15, 2013 Do Now:

3-1 Solving Systems of Equations by Graphing Objectives: 1)solve systems of linear equations by graphing 2) Determine whether a system of linear equations is consistent and independent, consistent and dependent, or inconsistent

System of Equations Consists of two or more equations with the same variables Solution is the ordered pair that satisfies all of the equations Can be solved using 3 methods: – Graphing – Elimination – Substitution

Example 1: Solve the system of equations by graphing. Graph each equation on the same plane and see where they intersect.

How can we verify that the solution is correct? Substitute the Solution into EACH equation

When two lines intersect, a system of equations has one solution (meaning only one point will satisfy the system). When a system has one solution, the system is said to be consistent and independent.

Example 2: Solve the system of equations by graphing

A system of equations might have no solution. – This would occur if the equations never intersect (they are parallel). – When a system of equations has no solution, the system is said to be inconsistent.

Example 3: Solve the system of equations by graphing.

A system of equations might have infinitely many solutions. – This would occur if the equations are the same exact line. – When a system of equations has infinitely many solutions, the system is said to be consistent and dependent.

Example 4: Solve the system of equations by graphing.

Example 5 : Solve the system of equations by graphing.

Why was graphing not a good method to use on the previous example? What other options do we have?

Substitution another method we can use to solve a system of equations. Steps: – 1) solve one equation for one variable (in terms of the other variable) – 2) substitute that expression into the other equation (replace the variable that you solved for in step 1) – 3) After you attain a numerical value for one variable, substitute back into one of the original equations to attain the numerical value for the other variable. **Your solution is still an ordered pair (or no solution or infinitely many solutions, depending on the system).**

Example 1: Use substitution to solve the system of equations.

Example 2: Use substitution to solve the system of equations.

Example 3 : Use substitution to solve the system of equations.

Examples 4 & 5: Use substitution to solve the system of equations.

Try These on your own…

when you end up with two constants that are not equal, there is no solution to the system. (If you graphed these two lines, they would be parallel.) when you end up with two constants that are equal, there are infinitely many solutions to the system. (If you graphed these lines, they would be the same line.)

Homework Text p. 113 #s13-34 (FIRST COLUMN ONLY) Show graphs for each Classify each system (checking is NOT necessary) p. 114 #s Text p. 120 #s all, #s 39-40