Question

$\begin{gathered}10x-16y=12 \\ 5x-3y=4\end{gathered}$

If $( x, y )$ is a solution to the system of equations above, what is the value of $x-y$?​​

Answer 1

EXPLANATION.

⇒ 10x - 16y = 12.

⇒ 5x - 3y = 4.

As we know that,

From equation (1) & (2), we get.

Multiply equation (1) by 5.

Multiply equation (2) by 10.

We get,

⇒ 10x - 16y = 12 --------(1) x 5.

⇒ 5x - 3y = 4 ------(2) x 10.

⇒ 50x - 80y = 60.

⇒ 50x - 30y = 40.

-      +          -

We get,

⇒ -50y = 20.

⇒ y = -2/5.

Put the value of y = -2/5 in equation, we get.

⇒ 5x - 3(-2/5) = 4.

⇒ 5x + 6/5 = 4.

⇒ 5x = 4 - 6/5.

⇒ 5x = 20 - 6/5.

⇒ 5x = 14/5.

⇒ x = 14/25.

To find : x - y.

⇒ 14/25 - (-2/5).

⇒ 14/25 + 2/5.

⇒ 14 + 10/25.

⇒ 24/25.

Value of : x - y = 24/25.

Answer 2

Answer :-

$\implies\sf 10x - 16y = 12 \: \: \: \: \: \: \: -i$

$\implies\sf 5x - 3y = 4 \: \: \: \: \: \: \: -ii$

Multiplying equation ii by 2 :-

$\implies\sf 2 ( 5x - 3y = 4 )$

$\implies\sf 10x - 6y = 8 \: \: \: \: \: \: \: -iii$

Subtracting equation iii from i :-

$\implies\sf 10x - 16y - ( 10x - 6y ) = 12 - 8$

$\implies\sf 10x - 16y - 10x + 6y = 4$

$\implies\sf -10y = 4$

$\implies\sf y = \dfrac{-4}{10}$

$\implies\boxed{\sf y = -0.4}$

Substituting the value in equation i :-

$\implies\sf 10x - 16y = 12$

$\implies\sf 10x - 16 \times ( -0.4 ) = 12$

$\implies\sf 10x + 6.4 = 12$

$\implies\sf 10x = 5.6$

$\implies\sf x = \dfrac{5.6}{10}$

$\implies\boxed{\sf x = 0.56}$

Finding the value of ( x - y )

$\implies\sf x - y = 0.56 - ( - 0.4 )$

$\implies\boxed{\sf x - y = 0.96}$