SOLUTION TO SIMULTANEOUS LINEAR EQUATIONS By Olowolafe Samuel Opeyemi(Opsam)

A variable in Mathematics can assume different values It is usually the unknown which we denote using letters A linear expression is a Mathematical statement which has the highest power of its variable(s) as E.g. 2x + 5y, a + 2p, -7c – d, etc. Solution To Simultaneous Linear Equations

  Solution To Simultaneous Equations

c – f = -4, 6v – 5r = 3, 7y + t – 3 = 0, 4e + 3 = 0, etc. A linear equation is an equation with the highest power of its unknown as E.g. c – f = -4, 6v – 5r = 3, 7y + t – 3 = 0, 4e + 3 = 0, etc. . Solution To Simultaneous Linear Equations

Simultaneous linear equations are two or more linear equations with at least two variables(unknowns) which could be solved at the same time. Simultaneous equations could be solved using graphical, elimination, substitution, Crammer, row reduction methods and many more Solution To Simultaneous Equations

Put x = 2 in (ii) USING THE ELIMINATION METHOD-Case 1         Put x = 2 in (ii) Solution To Simultaneous Linear Equations

  2 + y = 5   In conclusion, x = 2 and y = 3

x = 2 Put x = 2 in equation ii USING THE ELIMINATION METHOD- Case 1         x = 2 Divide both sides by 6 Put x = 2 in equation ii Solution To Simultaneous Linear Equations

In conclusion, x = 2 and y = -2     In conclusion, x = 2 and y = -2 Solution To Simultaneous Equations

a = 4 USING THE ELIMINATION METHOD- Case 1 Put a = 4 in equation ii         Divide both sides by 8 a = 4 Put a = 4 in equation ii

      Divide both sides by 3    

Exercise 1: Solve simultaneously using elimination method   Solution To Simultaneous Equations

x = 1/2, y = 7/2 x = -4, y = -5 p = 4, q = 22 m = 3, n = -7 ANSWERS TO EXERCISE 1 x = 1/2, y = 7/2 x = -4, y = -5 p = 4, q = 22 m = 3, n = -7 a = -3, b = 4 Solution To Simultaneous Equations

USING THE ELIMINATION METHOD- Case 2     X 5 X 6

      Divide both sides by 52   Solution To Simultaneous Equations

       

6p = 3 p = 3/6; p = 1/2 Divide both sides by 6   6p = 3 Divide both sides by 6 p = 3/6; p = 1/2 Solution To Simultaneous Equations

USING THE ELIMINATION METHOD- Case 2     X 2 X 3

      Divide both sides by -7   Solution To Simultaneous Equations

Collect like terms Put y = 1/7 in equation (ii)   Collect like terms     Solution To Simultaneous Equations

14x = 20 Divide both sides by 14 Cross multiply   Cross multiply 14x = 20 Divide both sides by 14   Solution To Simultaneous Equations

USING THE ELIMINATION METHOD- Case 2       X 6 X -3

      Divide both sides by 9   Put y = 4/9 in equation (i)

      Collect like terms

      Cross multiply -27x = 20 Divide both sides by - 27  

Exercise 2: Solve simultaneously using elimination method   Solution To Simultaneous Equations

ANSWERS TO EXERCISE 2  

USING THE SUBSTITUTION METHOD- CASE 1 AND 2       From (ii), make y the subject of the formula    

Put (iii) in (i) that is substitute y = 2 – 7x in (i)       Collect like terms   Solution To Simultaneous Equations

      Put x = 3 in (iii)         We can finally conclude that x = 3 and y = -19

USING THE SUBSTITUTION METHOD- CASE 1 AND 2       From (i), make n the subject of the formula  

Put (iii) in (ii) that is substitute n = 7m – 15 in (ii)   Put (iii) in (ii) that is substitute n = 7m – 15 in (ii)       Collect like terms   Solution To Simultaneous Equations

We can finally conclude that m = 1 and n = -8       Put m = 1 in (iii)         We can finally conclude that m = 1 and n = -8

From (i), make a the subject of the formula       From (i), make a the subject of the formula

    Divide both sides by 2   Solution To Simultaneous Equations

       

  Cross multiply     Collect like terms  

      Put b = -4 in (iii)    

      Solution To Simultaneous Equations

EXERCISE 3 Use the substitution method to solve the following simultaneous equations  

Solution To Exercise 3  

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