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 x 3 and 2 |
Coefficients of y 4 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 x 2 and 3 |
Coefficients of y 3 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.
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