Title: Algebra 1
Author: Mandy McDaniel
Last saved by: MHE

Lesson 5-3

Example 1     Elimination Using Addition
	Use elimination to solve each system of equations.
	-4x + 3y = 17
	4x + y = 3
Since the coefficients of the x-terms, -4 and 4, are additive inverses, you can eliminate the x-terms by adding the equations.
	-4x + 3y = 17	Write the equations in column form and add.
	(+)4x +  y =    3
	  4y = 20	Notice the x variable is eliminated.
	   = 	Divide each side by 4.
	   y = 5	Simplify.

	Now substitute 5 for y in either equation to find the value of x.
	4x + y = 3	Second equation
	4x + 5 = 3	Replace y with 5.
	4x + 5 – 5 = 3 – 5	Subtract 5 from each side.
	4x = -2	Simplify.
	 = 	Divide each side by 4.
	x = -	Simplify.
	
	The solution is .

Example 2 Write and Solve a System of Equations
Six times one number added to twice another number is –5. Negative six times the first number minus the other number is 7.
Let x represent the first number and y represent the second number.

-5  

is  

twice another number

added to 

Six times one number

	        6x	           +	             2y						 =	    -5

7

is 

the other number 

minus

Negative six times the first number

		                 -6x	           -			y							 =		 7
	Use elimination to solve the system.
		 6x + 2y = -5	Write the equations in column form and add.
		(+) -6x -   y =   7
			y =   2	The variable x is eliminated.
	Now substitute 2 for y in either equation to find the value of x.
		-6x -   y = 7	Second equation
		 -6x – 2 = 7	Replace y with 2.
	 -6x – 2 + 2 = 7 + 2	Add 2 to each side.
			-6x = 9	Simplify.
		 = 	Divide each side by –6.
		 x = -	Simplify.
	The numbers are - and 2.	

Example 3 Elimination Using Subtraction
	Use elimination to solve the system of equations.
	7a + 3b = 3
	2a + 3b = 18
Since the coefficients of the b-terms, 3 and 3, are the same, you can eliminate the b-terms by subtracting the equations.
	7a + 3b =    3	Write the equations in column form and subtract.
	(-)  2a + 3b =   18
		5a	= -15	The variable b is eliminated.
                    = 	Divide each side by 5.
	a = -3	Simplify.
	
Now substitute –3 for a in either equation to find the value of b.
	2a + 3b = 18	Second equation
	2(-3) + 3b = 18	a = -3
	 -6 + 3b = 18	Simplify.
	               3b = 24	Add 6 to each side and simplify.
		 = 	Divide each side by 3.
		 b = 8				The solution is (-3, 8).