SOLVING EQUATIONS BY SUBSTITUTION METHOD

In this page solving equations by substitution method we are going to see solution of first question in the worksheet of substitution method.

What does mean by substitution method:

Solving system of equation by substitution method, involves solving any one of the given equation for either 'x' or 'y' and plugging that in the other equation and solve that equation for another variable.

Solve the following equations using substitution method 

x - 5y + 17 = 0  and 2x + y + 1 = 0

Solution:

                        x - 5y + 17 =0 ----- (1)

                   2x + y + 1 = 0  ------(2) 

In the first equation coefficient of x is 1,in the second equation the coefficient of x is 2 and we have same signs for both equations. But the coefficient of y in the first equation is 5 and coefficient of y in the second equation is 1 and we have different signs.

To make the coefficient of y of the second equation as 5 we need to multiply the the whole equation by 5.Then we are going to add the first equation with second equation since we have different sign.

  (2) x 5            10x + 5y + 5 = 0

                         x - 5 y + 17 = 0  

                       10 x + 5 y + 5 = 0

                       ------------------

                        11 x  + 22 = 0

                       ----------------

                        11 x  = - 22

                          x = -22/11

                          x = -2

 Substituting x = -2 in the first equation

                         -2 - 5y + 17 = 0

                              -2 + 17 - 5 y = 0 

                                15 -5 y = 0  

                                -5 y = 0 - 15

                                -5 y = - 15

                                    y = -15/(-5)

                                    y = 3

Therefore the solution is

x = -2 and

y = 3   substitution method question1 substitution method question1

(1) Solve the following equations using substitution method x - 5y + 17 =0  and 2x + y + 1 = 0

Solution

(2) Solve the following equations using substitution method 5 x - 3 y - 8 = 0  and  2x - 3 y - 5  = 0

Solution

(3) Solving the following equations using substitution method   4 x - 7 y = 0  and 8 x - y - 26 = 0

Solution

(4) Solving the following equations using substitution method  3 x + 5 y - 6 =0  and 5 x - y - 10 = 0

Solution

(5) Solving the following equations using substitution method 2 x + 3 y =5  and 3 x + 4 y = 7

Solution

(6) Solving the following equations using substitution method  5 x + 6 y = 25  and 3 x - 4 y = 10

Solution

(7) Solving the following equations using substitution method 4 x - 3 y = 3  and 3 x + 2 y = 15

Solution

(8) Solving the following equations using substitution method 3 x + 2 y = 11 and 7 x - 3 y = 41

Solution

(9) Solving the following equations using substitution method  5 x + 3 y = 11  and 3 x + 5 y = -3

(10) Solving the following equations using substitution method  2 x - y = 15  and 5x + 3y=21

Solution