Warm Up Solve by graphing (in your calculator) 1) 2)

HW Check 5.3 1) a) y = -x + 9b) y = 2x – 3/2 c) y = 2/5x – 9/10d) y = -1/4x – 1/8 e) y = 2x – 3f) y = -2x – 8 2) Circle c & d a) y = 3x – 12 b) y = 3/2x + 9/2 3) a) m = 3/2 b= -6 b) m = 3/2 b = 4 c) m = 4 b = 8 d) m = 4 b = 9

Solving Systems by Substitution

Substitution Not every system can be solved easily by graphing. Sometimes it is not always clear from the graph where the solution is. We can use an algebraic method called SUBSTITUTION to find the exact solution without a graphing calculator.

Solving by Substitution Steps Step 1: Solve for one of the variables. Step 2: Substitute the expression of the equation you solved for into the other equation. Step 3: Solve for the variable. Step 4: Substitute the value of x into either equation and solve.

Example #1 Solve the system by substitution.

Example #2 Solve the system by substitution.

Example #3 Solve by substitution

Example #4

Example #5 Solve the system by substitution.

Example #6 - Try One! Solve the system by substitution.

Solving Systems by Elimination

Elimination We can solve by elimination by either Adding or Subtracting two equations to eliminate a variable!

Example Solve by Elimination

Example Solve by Elimination

Try Some! Solve the systems by elimination. 1.2.

Solving with Elimination Scalar Multiplication

More with Elimination Sometimes with elimination you will have to multiply one or both of the equations in a system. This creates an EQUIVALENT SYSTEM that has the same solution to the original.

Example Solve the system by elimination.

Special Solutions Solve each system by elimination. 1.2.