Systems of Equations

Systems of Equations Solve for X and Y X + Y=6, 2X + Y = 8 7X + 3Y = 14, 5X + 9Y = 10 4X + Y = 16, 2X + 3Y = 24 Y = 25, 8X - 2Y = 14 Using the elimination method for solving simultaneous equations we get X + Y=6, 2X + Y = 8 X + Y = 6 -- ( [1] 2X + Y = 8 -- ( [2] ( (Changing signs) Substituting X = 2 in [1] we get + y = 6 y = 6 -- 2 y = 4 Therefore x = 2 and y = 4 X and y values thus found can be verified by substituting them in any one of the given equations.

2X + Y = 8 L.H.S = R.H.S 7X + 3Y = 14, 5X + 9Y = 10 7X + 3Y = 14 -- ((1) 5X + 9Y = 10 -- >(2) Multiplying (1) by 5, we get 35x + 15y = 70 -- ( (3) Multiplying (2) by 7, we get 35x + 63y = 70 -- ( (4) (3)- (4),we get -48y = 0 y = 0 Substituting y = 0 in [1] we get 7x + 0 = 14 =>7x = 14 Therefore x = 2 and y = 0 X and y values thus found can be verified by substituting them in any one of the given equations. 5x + 9y = 10 5(2) + 9(0) = 10 10 + 0 = 10 L.H.S = R.H.S c.

4X + Y = 16, 2X + 3Y = 24 4X + Y = 16 -- ((1) 2X + 3Y = 24 -- ((2) Multiplying (1) by 3, we get 12X + 3Y = 48 -- ((3) (3)-(2), we get 10x = 24 => x = 2.4 Substituting x = 2.4 in (1) we get 4(2.4) + y = 16 9.6 + y = 16 => y = 16 -- 9.6 => y = 6.4 The values are X = 2.4, y = 6.4 Verification:- Substituting x = 2.4,y = 6.4 in (2) we get 2(2.4) + 3(6.4) = 24 4.8 + 19.2 = 24 L.H.S = R.H.S d.

12X + Y = 25, 8X - 2Y = 14 12X + Y = 25 -- ((1) 8X - 2Y = 14 -- ((2) Multiplying (1) by 2, we get 24x + 2y = 50 -- ((3) Adding (2) and (3), we get 32x = 64 Substituting x = 2 in (1) we get 12(2) + y = 25 24 + y = 25 =>y = 25 -- 24 =>y = 1 The values are X = 2, y = 1 Verification:- Substituting x = 2,y = 1 in (2) we get 8(2) -- 2(1) = 14 =>16 -- 2 = 14 L.H.S = R.H.S 2) Let x be the value of a share of Company X. Let y be the value of a share of Company Y.

The equations for Bob and Frank's holdings are 8000x + 6000y = 680000 -- ((1) 2000x + 10000y = 680000 -- ((2) In order to simplify the given equations we divide the above two equations by 1000 8x + 6y = 680 -- ((3) 2x + 10y =.