## ELIMINATION METHOD

The flow chart shown below explains the steps to be done in solving system of linear equations with two unknowns 'x' and 'y' using elimination method.  Example 1 :

Solve by elimination method.

3x + 4y  =  -25

2x - 3y  =  6

Solution :

3x + 4y  =  -25 ---- (1)

2x - 3y  =  6  ---- (2)

 Coefficients of x3 and 2 Coefficients of y4 and -3

Since the coefficients are not same, we can try to make them same by taking LCM.

Eliminating y  and solve for x :

LCM (3, 4) = 12

(1) ⋅ 3 ==> 9x + 12y = -75

(2) ⋅ 4 ==> 8x - 12y = 24

By observing the equations now, they are having different signs. So, we have to add them.

9x + 12y + 8x - 12y = -75 + 24

17x = -51

Dividing by 17 on both sides.

x = -51/17

x = -3

Finding the value of y :

By applying the value of x in (2), we get

2(-3) - 3y = 6

-6 - 3y = 6

Add 6 on both sides, we get

-3y = 12

Dividing by -3 on both sides.

y = -4

Example 2 :

Solve by elimination method

2x + 3y  =  5

3x + 4y  =  7

Solution :

2x + 3y  =  5  ----(1)

3x + 4y  =  7  ----(2)

 Coefficients of x2 and 3 Coefficients of y3 and 4

Since the coefficients are not same, we can try to make them same by taking LCM.

Eliminating y and solve for x :

LCM (2, 3) = 6

(1) ⋅ 3 ==> 6x + 9y = 15

(2) ⋅ 2 ==> 6x + 8y = 14

By observing the equations now, they are having same signs. So, we have to subtract them.

6x + 9y - 6x - 8y = 15 - 14

x = 1

Finding the value of y :

By applying the value of x in (1), we get

2(1) + 3y = 5

2 + 3y = 5

Subtracting 2 on both sides.

3y = 3

Dividing by 3 on both sides.

y = 1

Example 3 :

A park charges \$10 for adults and \$5 for kids. How many many adults tickets and kids tickets were sold, if a total of 548 tickets were sold for a total of \$3750 ?

Solution :

Step 1 :

Let "x" be the number of adults tickets and "y" be the number of kids tickets.

No. of adults tickets + No. of kids tickets  =  Total

x + y  =  548 ----(1)

Step 2 :

Write an equation which represents the total cost.

Cost of x no. adults tickets  =  10x

Cost of y no. of kids tickets  =  5y

Total cost  =  \$3750

Then, we have

10x + 5y  =  3750

Divide both sides by 5.

2x + y  =  750 ----(2)

Step 3 :

Solve (1) and (2) using elimination method.

x + y  =  548 ----(1)

2x + y  =  750 ----(2)

In the above two equations, y is having the same coefficient, that is 1.

Multiply the first equation by -1 to get the coefficient of -1. And keep the second equation as it is.

Then, we have

-x - y  =  - 548

2x + y  =  750

We can add the above two equations and eliminate y.

Then, we have

x  =  202

Step 4 :

Substitute 202 for x in the first equation.

(1)---->  202 + y  =  548

Subtract 202 from each side.

y  =  346

So, the number of adults tickets sold is 202 and the number of kids tickets sold is 346. Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.

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