Simultaneous equations

0

No comments posted yet

Comments

Slide 1

Solving Equations www.ipracticeMath.com

Slide 2

Determinant method of solving simultaneous equations If a, b, c and d are any four numbers, the value ad-bc is represented π‘Ž 𝑏 𝑐 𝑑

Slide 3

The value of the Determinant π‘Ž 𝑏 𝑐 𝑑 is ad-bc. As it has two rows and two columns It is called as determinant of order two www.ipracticeMath.com

Slide 4

where π‘Ž 1 , π‘Ž 2 , 𝑏 1 , 𝑏 2 , 𝑐 1 and 𝑐 2 are the real numbers such that π‘Ž 1 𝑏 2 βˆ’ π‘Ž 2 𝑏 1 β‰ 0 and 𝓍 and y are variables. simultaneous equations π‘Ž 1 π‘₯+ 𝑏 1 𝑦= 𝑐 1 π‘Ž 2 π‘₯+ 𝑏 2 𝑦= 𝑐 2 www.ipracticeMath.com

Slide 5

For equating the coefficients of y, let us multiply equation (1) by 𝑏 2 and equation (2) by 𝑏 1 to get, 𝒂 𝟏 𝒙+ 𝒃 𝟏 π’š= 𝒄 𝟏 𝒂 𝟐 𝒙+ 𝒃 𝟐 π’š= 𝒄 𝟐 𝒂 𝟏 𝒃 𝟐 𝒙+ 𝒃 𝟏 𝒃 𝟐 π’š= 𝒄 𝟏 𝒃 𝟐 ----------- 3 𝒂 𝟐 𝒃 𝟏 𝒙+ 𝒃 𝟏 𝒃 𝟐 π’š= 𝒄 𝟐 𝒃 𝟏 ----------- 4 www.ipracticeMath.com

Slide 6

Β  π‘Ž 1 𝑏 2 π‘₯+ 𝑏 1 𝑏 2 𝑦= 𝑐 1 𝑏 2 π‘Ž 2 𝑏 1 π‘₯+ 𝑏 1 𝑏 2 𝑦= 𝑐 2 𝑏 1 - - - π‘Ž 1 𝑏 2 βˆ’ π‘Ž 2 𝑏 1 π‘₯= 𝑐 1 𝑏 2 βˆ’ 𝑐 2 𝑏 1 Subtract equation (4) from equation (3), www.ipracticeMath.com

Slide 7

βˆ΄π“ = 𝑐 1 𝑏 2 βˆ’ 𝑐 2 𝑏 1 π‘Ž 1 𝑏 2 βˆ’ π‘Ž 2 𝑏 1 = 𝒄 𝟏 𝒃 𝟏 𝒄 𝟐 𝒃 𝟐 𝒂 𝟏 𝒃 𝟏 𝒂 𝟐 𝒃 𝟐 …(5) www.ipracticeMath.com

Slide 8

∴y = π‘Ž 1 𝑐 2 βˆ’ π‘Ž 2 𝑐 1 π‘Ž 1 𝑏 2 βˆ’ π‘Ž 2 𝑏 1 = π‘Ž 1 𝑐 1 π‘Ž 2 𝑐 2 π‘Ž 1 𝑏 1 π‘Ž 2 𝑏 2 …(6) www.ipracticeMath.com

Slide 9

D = π‘Ž 1 𝑏 1 π‘Ž 2 𝑏 2 𝑫 𝒙 = 𝒄 𝟏 𝒃 𝟏 𝒄 𝟐 𝒃 𝟐 𝑫 π’š = 𝒂 𝟏 𝒄 𝟏 𝒂 𝟐 𝒄 𝟐 www.ipracticeMath.com

Slide 10

From equations (5) and (6) Determinants we get, 𝓍 = 𝑫 𝒙 𝑫 and y = 𝑫 π’š 𝑫 This method of obtaining solution of simultaneous equations by using determinants is known as Cramer’s Rule.

Slide 11

Solve the following simultaneous equations using Cramer’s rule. The given equations are 5𝓍 –y = 5 5𝓍 + y = 15 www.ipracticeMath.com

Slide 12

D = πŸ“ βˆ’πŸ πŸ“ 𝟏 = 5 Γ— 1 – (-1 Γ— 5) = 5+ 5 = 10 𝑫 𝒙 = πŸ“ βˆ’πŸ πŸπŸ“ 𝟏 = 5 Γ— 1 – (-1 Γ— 15) = 5 + 15 = 20 𝑫 π’š = πŸ“ πŸ“ πŸ“ πŸπŸ“ =5 Γ— 15 – (5 Γ— 5) = 75 – 25 = 50 www.ipracticeMath.com

Slide 13

𝓍 = 𝑫 𝒙 𝑫 = 𝟐𝟎 𝟏𝟎 = 10 y = 𝑫 π’š 𝑫 = πŸ“πŸŽ 𝟏𝟎 = 5 ∴ 𝓍 = 10 and y = 5 is the solution of the given simultaneous equations.

Slide 14

www.iPracticeMath.com All Math Topic Algebra Basic Math Calculus Consumer Math 30 Minutes Math practice every day with www.ipracticeMath.com

Summary: www.iPracticeMath.com provides best Math help for every topic. This presentation shows Determinant method of solving simultaneous equations. Welcome to join us at: http://www.facebook.com/iPracticeMath

Tags: simultaneous equations determinant method real numbers variables multiply equation subtract cramer’s rule algebra math practice

URL: