8.3/8.4 Solving Systems by Elimination HOW DO YOU SOLVE A SYSTEM OF EQUATIONS BY ADDING OR SUBTRACTING?

In your given notes … DO NOT COPY THIS  Solving a system of two equations in two unknowns by elimination can be done by adding or subtracting one equation from the other.

Copy this underneath the paper you taped in A. Elimination by Adding Solve the system: 1. Eliminate the opposites (4y. -4y) 2. Combine the terms (x terms in this case) 3. Solve for x; 4. Plug x value into original equation to find the y 5. Write Solution x + 4y= 8 3x - 4y= 8 4x =16 4 X = 4 (4) + 4y=8 -4 4y = 4 4 Y = 1 Solution (4, 1)

Example 2x – 3y = 12 x + 3y = 6 = X = 2x – 3y = 12 2( )-3y= y=12 -3y = 0 Y = Solution (, )

Your Turn on slates  Look in page 244 from your textbook: X + y = -12x +2y = -2 X – y = 73x – 2y = 12{ {

B. Elimination by Multiplying a Negative Solve the system: 1. Multiply 1 equation by a negative (changing the signs of each term in the equation) 2. Eliminate opposites 3. Combine the terms 4. Solve for variable; 5. Plug variable value into original equation to find the y 6. Write Solution 2x - 5y = 15 2x + 3y = -9 {

Ex) 2x - 10y = -14 2x + 4y = 14

Ex) 3x + y = 17 3x – 2y = 2

Ex) X - 2y = -8 5x + 2y = -16

Can you use addition or subtraction to solve any system?  No, addition or subtraction can be used when the coefficients of the x- terms or the y-terms are the same or opposites.

8.4 Solving Systems by Elimination by Multiply? HOW DO YOU SOLVE A SYSTEM OF EQUATIONS BY ADDING OR SUBTRACTING?

What do you do if there aren’t any inverse variable terms or any like variable terms? 1. Decide which variable term to eliminate 2. Multiply one equation by a constant so you can eliminate a variable and combine other terms 3. Solve system using elimination method.

Example 2x + 10y = 2 (3x – 5y = -17)2 Multiply equation by 2 to eliminate the y terms 2x + 10y = 2 Rewrite 6x – 10 y = -34 Eliminate y-values; Solve for x; 8x = -32; x = -4 ? ? Plug in x to find y: 2(-4) + 10y = y = y = 10 Y = 1 Solution (-4, 1)

Example 5x + 2y = -10 3x + 6y = 66 -3(5x + 2y = -10) 3x + 6y = x – 6y = 30 3x + 6y = x = 96; x = -8 Which term will be easier to eliminate?

Example 3x + y = 0 2x + 4y = 30

Your Turn pg. 254 # 7 6x – 9y = 9 3x – 7y = 2

Your Turn pg. 254 # 8 -3x + y = 11 2x + 3y = -11

Word Problems Cut out the Your Turn Problems from page 231 and glue into INB. C. Setting Up Systems Using Word Problems 1.) Decide which two items are being compared – Write the equation in standard form (ax + by = c) 2.) Write an equation (in standard form) showing the money spent on the items. 3.) Solve the system using either graphing or elimination method.