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Solve, Using Cross-multiplication : 6x + 7y - 11 = 0 5x + 2y = 13 - Mathematics

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प्रश्न

Solve, using cross-multiplication :
6x + 7y - 11 = 0
5x + 2y = 13

योग

उत्तर

Given equation are 6x + 7y - 11 = 0 and 5x + 2y = 13
Comparing with a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0, We have

a1 = 6, b1 = 7, c1 = -11 and a2 = 5, b2 = 2, c2 = -13

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 = `[ 7 xx ( - 13) - 2 xx ( - 11 )]/[ 6 xx 2 - 5 xx 7 ]  and  y = [ - 11 xx 5 - ( - 13 ) xx 6 ]/[ 6 xx 2 - 5 xx 7 ]`

⇒ x = `[ - 91 + 22 ]/[ 12 - 35 ]  and y = [ - 55 + 78 ]/[ 12 - 35 ]`

⇒ x = `[ - 69 ]/[ -23 ]  and y = [ 23 ]/[ -23 ]`
⇒ x = 3 and y = -1

shaalaa.com
Methods of Solving Simultaneous Linear Equations by Cross Multiplication Method
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 6: Simultaneous (Linear) Equations (Including Problems) - Exercise 6 (C) [पृष्ठ ८५]

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सेलिना Concise Mathematics [English] Class 9 ICSE
अध्याय 6 Simultaneous (Linear) Equations (Including Problems)
Exercise 6 (C) | Q 3 | पृष्ठ ८५
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