University:
Missouri State University
Course:
MTH 103 | Intermediate Algebra
Academic year:

2020
Views:

301

Pages:

2
Author:

Graje8mk

ALGEBRA 2 Name KEY 3.3 SYSTEMS: ELIMINATION METHOD Date Block Solving Systems of Equations Algebraically: Elimination • Line up equations so x is over x and y is over y • Multiply the equations to make the coefficients of x or y opposite of each other • Add the two equations (one variable should be eliminated) • Solve for the remaining variable • Plug the answer into either equation • Write the answer as an ordered pair (x, y). Solve each system by elimination. 1) (2, - 2) x + 2y = - 2 3x - 2y = 10 x/4 = 8/4 X = 2 - y + 2y = - 2 (2y)/2 = - 4/2 Y = - 2 2) (-7,2) x = 3y - 13; - x = - 4y + 15 f - 3y = - 13 x + 4y = 15 y = 2y x = 3(2) - 13 x = 4 - 13 x = - 1 3) (-23) - 11(5x + 3y = - 1) \\ -4x+8y=17 - 5x - 7y = 1 (- 9x)/- 9 = 18/- 9 x = - 2 5(- 2) + 5y = - 1 - 10 + 3y = - 1 (3y)/R = 9/y y = 30 4) (-22) -3[ (2x + 3y = 2) 2( (3x - 4y = - 14) 0y - 9y = - 6 x - 8y = - 28 (- 17y)/- 17 = - 34/- 17 y = 2 2x + 3(z) = 2 2x + y = 2; - - 2/6 4/4 * x = - 4/2 x = - 2 5) (-2,3) int 2x - 5y = - 19 ) 3x + 2y = 0 ) 6x - 15y = - 57 6x - 4y = 0 (- 19y)/- 141 = - 57/- 19 Y = 3 2x - 5(3) = - 19 aligned x- sqrt 5 =-19\\ ** 15 aligned (2x)/2 = 4/2 (2) 6) (3,1) 3 (17x - 4y = 17) -1 ( (3x + 5y = 14) - 12y = 51 x - 35y = - 98 y = - 17 y = 1 3x + 5(1) = 14 3x + 5 = 14 sqrt(5 - 5) 3x = 9 x = 3 CLASSWORK 1. x 4y = 10; x - y = 2 (7x)/7 = 12/2 x = 6 ) 4 + y = 10 y = 4 (6,4) 2. x - 3y = - 13; - x + 4y = 15 y = 2 x - 3(2) = - 13 x - 6 = - 13 عام x = - 7 (-7,2) 4x + 2y = 2; 5x + 2y = 4 (- x)/- 1 = - 2/- 1 X = 2 (2,-3) 4(2) + 2y = 2 - 8/8 + 2y = 2/8 (xy = - 6)/2 =-3 5x-2y=3 - + y = - 9 ) (- 3y)/- 3 = 12/- 3 y = - 4 5x - 2(- 4) - 3 x + 6/5 = 3/5 5/4 = - 5/5 y = - 1 (-1,-4) 5= 3x+2y=8\\ 2x - 6y = 42 ) 9x + 6y = 24 (Nx)/11 = 66/11 x = 6 3(varphi) + 2y = 8 7 + 2y = 8; 7 - 18 (4y)/z = - 10/2 y = - 5 (6,-5) 4x + 2y = - 1; 6y + 3y = - 9 y 2-8y=4 (- 5y)/- 5 = - 5/- 5 y = 1 x + 2(1) = - 1 x + 2 = - 1 \\ -2-2 aligned x = - 3 (-3,1) -3 * 3x + 4y = 22; x - 5y = - 37 ) 3)(+ 4y = 22; - 7x + 15y = 111 19/19 = 133/19 y = 7 x - 5(7) = - 37 x - 32 = - 37 + - 55 + 35 x = - 2 (-2,7) 8. 2x + y = - 1; 7x - 5y = 5 10x + 5y = - 5 (17x)/17 = 0/17 x' = 0 2l0j + y = - 1 0 + y = - 1 y = - 1 (0,-1)