Question

15x - 14y = 117 and 14x - 15y = 115 ; solve by elimination method. i need this solution please ......

Answer 1

15x - 14y = 117 .......(1) let it be equation 1

14x - 15y = 115 ......(2) let it be equation 2

Adding both the equations (1) and (2) we get ,

15x - 14y = 117
(+) 14x - 15y = 115
----------------------
29x - 29y = 232

Dividing both sides by 29 we get

x - y = 8 .......... (3)

Now subtracting equation (2) from (1) we get ,


15x - 14y = 117
(-) 14x - 15y = 115
----------------------
x + y = 2 .........(4)

Now Adding equation 3 and 4 we get,

x - y = 8
(+) x + y = 2
-------------
2x = 10
hence, x = 5

x + y = 2
5 + y = 2
y = 2-5
= -3
Hence x = 2 and y = -3

Answer 2

Answer:

x = 5

y = -3

Step-by-step explanation:

• ELIMINATION METHOD:  One of the methods to solve linear equations is the elimination method.

1. In this method we must first convert the two equations such that it has the same coefficient either for variable x or variable y.
2. This can be done by multiplying both equations with a suitable number such that, the coefficient is the same.
3. By doing this we can convert the equation in two variables to an equation in one variable.

Equation 1: 15x-14y = 117

Equation 2: 14x-15y = 115

Now, we will multiply equation 1 with 14 and equation 2 with 15.

We get that,

210x-196y = 1638

210x-225y = 1725

Now subtract the two new equations and we get the value of y.

(210x-225y)-(210x-196y) = 1725 - 1638

-29y = 87

y = -3

By, substituting the value of y in the previous first equation:

15x-14(-3) = 117

15x + 22 = 117

15x = 75

x = 5

Hence, the value of x and y on solving is 5 and -3 respectively.

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