LESSON 2 8 SOLVING SYSTEM OF EQUATIONS BY

LESSON 2. 8 SOLVING SYSTEM OF EQUATIONS BY SUBSTITUTION Concept: Solving Systems of Equations EQ: How can I manipulate equation(s) to solve a system of equations? (REI. 5) Vocabulary: System of equations, consistent (independent/dependent), substitution, ordered pair

KEY CONCEPTS There are various methods to solving a system of equations. A few days ago we looked at the graphing method. Today we are going to look at the substitution method. The substitution method involves solving one of the equations for one of the variables and substituting that into the other equation. Solutions to systems are written as an ordered pair, (x, y). This is where the lines would cross if graphed.

KEY CONCEPTS CONTINUED If the solution is a true statement, such as 9 = 9, then the system has an infinite number of solutions. This is where the lines would coincide if graphed. If the solution is an untrue statement, such as 4 = 9, then the system has no solutions. This is where lines would be parallel if graphed. Check your answer by substituting the x and y values back into the original equations. If the answer is correct, the equations will result in true statements.

STEPS FOR SUBSTITUTION METHOD Step 1: Solve one of the equations for one of its variables. Step 2: Substitute the expression from step 1 into the other equation. Step 3: Solve the equation from step 2 for the other variable. Step 4: Substitute the value from step 3 into the revised equation from step 1 (or either of the original equations) and solve for the other variable.

Isolate y by subtracting x from both sides.

Second equation of the system. Simplify. Add 2 to both sides. Divide both sides by 2.

Revised equation from step 1. Simplify.

Second equation of the system. Simplify. Add 12 to both sides. Divide both sides by 5.

Revised equation from step 1. Simplify.

YOU TRY!