Given equation are 8x + 5y = 9 and 3x + 2y = 4 a1 = 8, b1 = 5, c1 = -9 and a2 = 3, b2 = 2, c2 = - 4 Now, x = `[ b_1c_2 - b_2c_1 ]/[ a_1b_2 - a_2b_1 ] and y = [ c_1a_2 - c_2a_1 ]/[ a_1b_2 - a_2b_1 ]` ⇒ x = `[ 5 xx ( - 4 ) - 2 xx ( - 9 )]/[ 8 xx 2 - 3 xx 5 ] and y = [ - 9 xx 3 - ( - 4 ) xx 8 ]/[ 8 xx 2 - 3 xx 5 ]` ⇒ x = `[ - 20 + 18 ]/[ 16 - 15 ] and y = [ - 27 + 32 ]/[ 16 - 15 ]` ⇒ x = `-2/1 and y = 5/1` Page 2Given equation are 4x - 3y - 11 = 0 and 6x + 7y - 5 = 0 a1 = 4, b1 = - 3, c1 = -11 and a2 = 6, b2 = 7, c2 = - 5 Now, x = `[ b_1c_2 - b_2c_1 ]/[ a_1b_2 - a_2b_1 ] and y = [ c_1a_2 - c_2a_1 ]/[ a_1b_2 - a_2b_1 ]` ⇒ x = `[ - 3 xx ( - 5 ) - 7 xx ( - 11 )]/[ 4 xx 7 - 6 xx ( - 3 ) ] and y = [ - 11 xx 6 - ( - 5 ) xx 4 ]/[ 4 xx 7 - 6 xx ( - 3) ]` ⇒ x = `[ 15 + 77 ]/[ 28 + 18 ] and y = [ - 66 + 20 ]/[ 28 + 18 ]` ⇒ x = `92/46 and y = - 46/46` ⇒ x = 2 and y = - 1 Page 3Given equation are 4x + 6y = 15 and 3x - 4y = 7 a1 = 4, b1 = 6, c1 = -15 and a2 = 3, b2 = - 4, c2 = -7 Now, x = `[ b_1c_2 - b_2c_1 ]/[ a_1b_2 - a_2b_1 ] and y = [ c_1a_2 - c_2a_1 ]/[ a_1b_2 - a_2b_1 ]` ⇒ x = `[ 6 xx (-7) - ( - 4 ) xx ( - 15 )]/[ 4 xx (-4) - 3 xx 6 ] and y = [ - 15 xx 3 - ( - 7 ) xx 4 ]/[ 4 xx ( - 4 ) - 3 xx 6 ]` ⇒ x = `[ - 42 - 60 ]/[ -16 - 18] and y = [ - 45 + 28 ]/[ - 16 - 18 ]` ⇒ x `(-102)/-34 and y = (-17)/(-34)` ⇒ x = 3 and y = `1/2` Page 4Given equation are 0.4x - 1.5y = 6.5 and 0.3x + 0.2y = 0.9 a1 = 0.4, b1 = -1.5, c1 = -6.5 and a2 = 0.3, b2 = 0.2, c2 = 0.9 Now, x = `[ b_1c_2 - b_2c_1 ]/[ a_1b_2 - a_2b_1 ] and y = [ c_1a_2 - c_2a_1 ]/[ a_1b_2 - a_2b_1 ]` ⇒ x = `[( - 1.5) xx (-0.9) - ( 0.2 ) xx ( -6.5 )]/[ 0.4 xx (0.2) - (0.3) xx (-1.5) ] and y = [ (-6.5) xx (0.3) - (-0.9) xx (0.4) ]/[ 0.4 xx ( 0.2) - (0.3) xx (-1.5) ]` ⇒ x = `[ 1.35 + 1.3 ]/[ 0.08 + 0.45 ] and y = [ -1.95 + 0.36 ]/[ 0.08 + 0.45 ]` ⇒ x = `2.65/0.53 and y = (-1.59)/(0.53)` ⇒ x = 5 and y = - 3 Page 5Given equation are √2x - √3y = 0 and √5x + √2y = 0 a1 = √2, b1 = √3, c1 = 0 and a2 = √5, b2 = √2, c2 = 0 Now, x = `[ b_1c_2 - b_2c_1 ]/[ a_1b_2 - a_2b_1 ] and y = [ c_1a_2 - c_2a_1 ]/[ a_1b_2 - a_2b_1 ]` ⇒ x = `[ (-sqrt3) xx 0 - sqrt2 xx 0 ]/[ sqrt2 xx sqrt2 - sqrt5 xx (-sqrt3) ] and y = [ 0 xx sqrt5 - 0 xx sqrt2 ]/[ sqrt2 xx sqrt2 - sqrt5 xx ( - sqrt3 ) ]` ⇒ x = `0/[ 2 + sqrt15 ] and y = 0/[ 2 + sqrt15 ]` ⇒ x = 0 and y = 0. Given equations 8x + 5y = 9 …………………..(1) 3x + 2y = 4 ……………….….(2) From equation (2) we obtain the value of x as x = (4 – 2y )/ 3 ……………… (3) Subatituting x = (4 – 2y )/ 3 in equation 1, we get 8(4-2y)/3 + 5y = 9 32 – 16y +15y = 27 -y = -5 y = 5 ……….(4) Substituting y=5 in in equation (2), we get 3x + 10 = 4 x = -2 Hence, x = -2 and y = 5 By Cross Multiplication method: 8x +5y – 9 = 0 3x + 2y – 4 = 0 On cross multiplying both the equations we get x/(-20+18) = y/(-27 + 32 ) = 1/(16-15) -x/2 = y/5 =1/1 -x/2 =1 => x=-2 y/5 =1=>y=5 Therefore, x = -2 and y =5.
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Last updated at July 24, 2021 by Teachoo
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