# Solve the set of equations 3x - 2y = 10 and 4x - y = 5 only using elimination

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The following set of equations has to be solved :

3x - 2y = 10 ...(1)

4x - y = 5 ...(2)

4*(1) - 3*(2)

=> 12x - 8y - 12x + 3y = 40 - 15

=> -5y = 25

=> y = -5

(1) - 2*(2)

=> 3x - 8x - 2y + 2y = 10 - 10

=> -5x = 0

=> x = 0

**The solution of the given set of equations is x = 0 and y = -5**

3x-2y=10---------(i)

4x-y=5-----------(ii)

now, multiplying equation (ii) by 2 we get

8x-2y= 10--------(iii)

3x-2y=10---------(i)

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

5x=0 By subtracting (i) from (ii)

x= o

now , by putting the value of x in (ii) we get

y=4x-5

y=4*0-5

y=-5

Therefore , the required value of x and y are (0 , -5).

Let:

3x - 2y = 10---------(i)

4x - y = 5-----------(ii)

In order to use the method of elimination we need to make the value of one of the variables, that is either x or y, equal in both the equations so as to eliminate that variable.

Hence, we multiply the second equation by 2:

2 (4x-y) = 2 X 5

8x - 2y = 10

Now we combine both the equations by using subtraction method of elimination:

3x - 2y - (8x - 2y) = 10 - 10

3x -2y - 8x +2y = 0

3x - 8x -2y + 2y = 0

-5x = 0

Dividing each side by -5:

-5x/-5 = 0/-5

Therefore, x = 0

Now in order to find out the value of y, we put the value of x into any of the two original equations, here we put the value of x in equation (i):

3x - 2y = 10---------(i)

3(0) - 2y = 10

0 - 2y = 10

-2y = 10

y = - 10/2

y= -5

**Therefore, x=0, and y=-5**

In order to check the answers, we put the values in both the equations:

3x - 2y = 10---------(i)

3(0) - 2(-5) = 10

0 + 10 = 10

10 = 10

Since, left hand side and right hand side are equal. Hence proved.

4x - y = 5-----------(ii)

4(0) - (-5) = 5

0 + 5 = 5

5 = 5

Since, left hand side and right hand side are equal. Hence, proved.