Solving a System of Equations in Two Variables By Elimination Chapter 8.3

Steps to solve a system of equations using the elimination method 1.The coefficients of one variable must be opposite. 2.You may have to multiply one or both equations by an integer so that step 1 occurs. 3.Add the equations so that a variable is eliminated. 4.Solve for the remaining variable. 5.Substitute the value into one of the original equations to solve for the other variable. 6.Check the solution.

3x 5x step 1 coefficients of one variable must be opposite. 1. Solve by addition. + y = 7 – 2y = 8

2( ) 6x + 2y = 14 5x – 2y = 8 step 2 make the y opposites, multiply first equation by Solve by addition. 3x 5x + y = 7 – 2y = 8

2( ) 6x + 2y = 14 5x – 2y = 8 11x = 22 step 3 add to eliminate the y. 1. Solve by addition. 3x 5x + y = 7 – 2y = 8

2( ) 6x + 2y = 14 5x – 2y = 8 11x = x = 2 step 4 solve for x. 1. Solve by addition. 3x 5x + y = 7 – 2y = 8

2( ) 6x + 2y = 14 5x – 2y = 8 11x = x = 2 3(2) (2, 1) 6 + y = 7 y = 1 step 5 substitute into equation 1 and solve for y. 1. Solve by addition. + y= 7 3x 5x + y = 7 – 2y = 8

4x 3x step 1 coefficients of one variable must be opposite. 2. Solve by addition. + 5y = y = 12

-4( ) 3( ) 12x + 15y = x – 28y = -48 step 2 make the x opposites, multiply first equation by 3, second equation by Solve by addition. 4x 3x + 5y = y = 12

-4( ) -13y = 3 step 3 add to eliminate the x. 2. Solve by addition. 3( ) 12x + 15y = x – 28y = -48 4x 3x + 5y = y = 12

-4( ) step 4 solve for y. 2. Solve by addition. -13y = 3 3( ) 12x + 15y = x – 28y = -48 y = x 3x + 5y = y = 12

-4( ) 52x 13( ) step 5 substitute into equation 1 and solve for x. 2. Solve by addition y = 3 3( ) 12x + 15y = x – 28y = -48 y = x + ( ) = x = x = (, ) – 15= ( ) = 17 4x 4x 3x + 5y = y = 12

( ) 12 xx -2x Before beginning with the steps remove the fractions in the first equation by multiplying 12 to each term. 3. Solve by addition. 8x – 9y= 36 step 1 coefficients of one variable must be opposite. –  y = 3 + y= 6

4( ) 12( ) 3. Solve by addition. 8x – 9y= 36 step 2 make x opposites, multiply second equation by 4. -8x + 4y= 24 xx -2x –  y = 3 + y= 6

4( ) 3. Solve by addition. 12( ) 8x – 9y= 36 -8x + 4y= 24 -5y = 60 step 3 add to eliminate the x. xx -2x –  y = 3 + y= 6

4( ) 12( ) 3. Solve by addition. 8x – 9y= 36 -8x + 4y= 24 -5y = step 4 solve for y. y = - 12 xx -2x –  y = 3 + y= 6

4( ) 12( ) 3. Solve by addition. 8x – 9y= 36 -8x + 4y= 24 -5y = step 5 substitute into equation 2 and solve for x. y = x x = ( - 12)= 6 x = - 9 ( - 9, - 12) xx -2x –  y = 3 + y= 6

( ) ( ) x 0.5x Before beginning with the steps remove the decimals by multiplying 10 to each term in each equation. 4. Solve by addition. 2x + 3y= - 1 step 1 coefficients of one variable must be opposite. 5x – y= y= – 0.1y= - 1.1

3( ) 4. Solve by addition. 2x + 3y= - 1 step 2 make y opposites, multiply second equation by 3. 5x – y= x + 3y = x – 3y= - 33

3( ) 4. Solve by addition. 2x + 3y= - 1 5x – y= x + 3y = x – 3y= x = - 34 step 3 add to eliminate the y.

3( ) 4. Solve by addition. 2x + 3y= - 1 5x – y= x + 3y = x – 3y= x = step 4 solve for x. x = - 2

3( ) 4. Solve by addition. 2x + 3y= - 1 5x – y= x + 3y = x – 3y= x = x = - 2 step 5 substitute into equation 1 and solve for y. 2( - 2) y = y= - 1 y = 1 ( - 2, 1) y = - 1

Solving a System of Equations in Two Variables By Elimination Chapter 8.3