System of Equations Adapted by Mrs. Garay

Warm Up Solve for the indicated variable. 1. P = R – C for R 2. V = Ah for A 3. R = for C R = P + C Rt + S = C 1 3 C – S t = A 3V3V h

mxlaZWQ mxlaZWQ

Learn to solve systems of equations.

Vocabulary system of equations solution of a system of equations

A system of equations is a set of two or more equations that contain two or more variables. A solution of a system of equations is a set of values that are solutions of all of the equations. If the system has two variables, the solutions can be written as ordered pairs.

When solving systems of equations, remember to find values for all of the variables. Caution!

Example 1A: Solving Systems of Equations Solve the system of equations. y = 4x – 6 y = x + 3 y = 4x – 6y = x + 3 The expressions x + 3 and 4x – 6 both equal y. So by the Transitive Property they are equal to each other. 4x – 6 = x + 3

Additional Example 1A Continued To find y, substitute 3 for x in one of the original equations. y = x + 3 = = 6 The solution is (3, 6). Solve the equation to find x. 4x – 6 = x + 3 – x – xSubtract x from both sides. 3x – 6 = 3 3x Add 6 to both sides. 3 = 3 x = 3 Divide both sides by 3.

The system of equations has no solution. 2x + 9 = –8 + 2x – 2x – 2x Transitive Property Subtract 2x from both sides. 9 ≠ –8 Example 1B: Solving Systems of Equations y = 2x + 9 y = –8 + 2x

YOUR TURN! Solve the system of equations. y = x – 5 y = 2x – 8

How did you do? To find y, substitute 3 for x in one of the original equations. y = x – 5 = 3 – 5 = –2 The solution is (3, –2). Solve the equation to find x. x – 5 = 2x – 8 – x Subtract x from both sides. –5 = x – 8 3 = x + 8 Add 8 to both sides.

The system of equations has no solution. 3x – 7 = 6 + 3x – 3x – 3x Transitive Property Subtract 3x from both sides. –7 ≠ 6 YOUR TURN AGAIN! y = 3x – 7 y = 6 + 3x HOW DID YOU DO?

NOW IT IS TIME TO PRACTICE!