Section 8.4

What we are Learning:Solving systems of equations using elimination by

multiplicationDetermine the best method for solving systems of equations

Which Method Should You Use to Solve a System of Equations?

Method The Best Time to Use

Graphing If you want to estimate the solution, since graphing usually does not give an exact solution

Substitution If one or both of the equations are solved for one variable

Addition If one of the variables has opposite coefficients in the two equations

Subtraction If one of the variables has the same coefficient in the two equations

Multiplication If one of the variables in an equation has a coefficient that is a multiple of the coefficient of the same variable in the other equation so that addition or subtraction then eliminates the variable; ***You may have to multiply each equation by different numbers to create coefficients that are the same for a variable!!!!

Elimination by Multiplication:• Make sure that equations are written in the same

form.– Terms that have a variable in common need to be on

the same side of the equation• Determine if the coefficients have a factor in

common– Multiply each equation by the factor that will create a

term with the same coefficient.• Be sure that one of the terms is positive and the other is

negative

• Solve the system of equations using elimination

Examples:• 4x + 7y = 6 (-3) why?

6x + 5y = 20 (2) why?

-12x – 21y = -18 12x + 10y = 40 -11y = 22

-11y/-11 = 22/-11y = -2

4x + 7(-2) = 64x -14 = 64x -14 + 14 = 6 + 144x = 204x/4 = 20/4x = 5Solution: (5, -2)

• 4x – 3y = 12 x + 2y = 14 (-4) why?

4x – 3y = 12-4x – 8y = -56 -11y = -44

-11y/-11 = -44/-11y = 4

4x – 3(4) = 124x – 12 = 124x – 12 + 12 = 12 + 124x = 244x/4 = 24/4x = 6Solution: (6, 4)

Let’s Work These Together:

• 9x = 5y – 23x = 2y – 2

2x + 3y = 204x + 7y =16

Let’s Work This Together:

6x – 5y = 273x + 10y = -24

2x – 3y = 25x + 4y = 28

Let’s Work This Together

• The difference of four times a number and three times a second number is twelve. The first number added to two times the second number is 14. Find the two numbers.

Homework:

• Page 479– 15 to 23 odd– 29, 31