Question

5x - Зу = 1 solve the following pair
3х - у = 5 of equations by elimination method​

Answer 1

Given :-

» 5x - 3y = 1

➡ 5x - 3y - 1 = 0 ------(i)

» 3x - y = 5

➡ 3x - y - 5 = 0 ------(ii)

Multiplying equation (i) by 3 and equation (ii) by 5, we get

➡ 15x - 9y - 3 = 0 -------(iii)

➡ 15x - 5y - 25 = 0 -------(iv)

Subtracting equation (iv) from equation (iii)

➡ (15x - 9y - 3) - (15x - 5y - 25) = 0

➡ 15x - 9y - 3 - 15x + 5y + 25 = 0

➡ 15x - 15x - 9y + 5y - 3 + 25 = 0

➡ -4y + 22 = 0

➡ -4y = -22

➡ y = -22/-4

➡ y = 11/2

Putting value of y = 11/2 in equation (i)

➡ 5x - 3(11/2) = 1

➡ (10x - 33)/2 = 1

➡ 10x - 33 = 2

➡ 10x = 2 + 33

➡ 10x = 35

➡ x = 35/10 = 7/2

Hence, the value of x = 7/2 and y = 11/2

Answer 2

We have , 5x - 3y = 1

5x - 3y - 1 = 0 [Equation 1]

We also have , 3x - y = 5

3x - y - 5 = 0 [Equation 2]

Multiply Equation 1 with '3' and Equation 2 with '5 '

From the above step we get ...

▪️ 15x - 9y - 3 = 0 [Equation 3]

▪️ 15x - 5y - 25 = 0 [Equation 4]

Now , Subtract equation 4 from equation 3

$\implies{(15x - 9y - 3) - (15x - 5y - 25) = 0}$

$\implies{15x - 9y - 3 - 15x + 5y + 25 = 0}$

$\implies{15x - 15x - 9y + 5y - 3 + 25 = 0}$

$\implies{ -4y + 22 = 0}$

$\implies{ -4y = -22}$

$\implies{y = -22/-4}$

$\implies{y = 11/2}$

Substituting value of y = 11/2 in equation 1 we get

$\implies{5x - 3(11/2) = 1} \\ </p><p></p><p> \implies{(10x - 33)/2 = 1} \\ </p><p></p><p> \implies{10x - 33 = 2} \\ </p><p></p><p> \implies{10x = 2 + 33} \\</p><p></p><p> \implies{ 10x = 35} \\</p><p> \implies{ x = 35/10 } \\ </p><p> \implies{x = 7/2}$

Therefore ,

Value of x = 7/2

Value of y = 11/2