Question

x/6+y/15=4,x/3-y/12=19/4

Answer 1

The value of x is 18 and y is 15.

Step-by-step explanation:

We have,

$\dfrac{x}{6}+\dfrac{y}{15}=4\ ......(1)$

and

$\dfrac{x}{3}-\dfrac{y}{12}=\dfrac{19}{4}\ ...(2)$

Equation (1) can be rewritten as :

$\dfrac{x}{6}+\dfrac{y}{15}=4\\\\\dfrac{5x+2y}{30}=4\\\\5x+2y=120\ .......(3)$

Equation (2) can be rewritten as :

$\dfrac{x}{3}-\dfrac{y}{12}=\dfrac{19}{4}\\\\4x-y=57\ .....(4)$

Now multiplying equation (4) by 2 such that we will have,

$8x-2y=114\ .....(5)$

Now adding equation (3) and (5) we get :

$13x=234\\\\x=18$

Put x = 18 in equation (4),

$4(18)-y=57\\\\y=15$

So, the value of x is 18 and y is 15.

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Answer 2

Step-by-step explanation:

\dfrac{x}{6}+\dfrac{y}{15}=4\ ......(1)

6

x

+

15

y

=4 ......(1)

and

\dfrac{x}{3}-\dfrac{y}{12}=\dfrac{19}{4}\ ...(2)

3

x

−

12

y

=

4

19

...(2{x}{6}+\dfrac{y}{15}=4\\\\\dfrac{5x+2y}{30}=4\\\\5x+2y=120\ .......(3)\end{gathered}

6

x

+

15

y

=4

30

5x+2y

=4

5x+2y=120 .......(3)

Equation (2) can be rewritten as :

\begin{gathered}\dfrac{x}{3}-\dfrac{y}{12}=\dfrac{19}{4}\\\\4x-y=57\ .....(4)\end{gathered}

3

x

−

12

y

=

4

19

4x−y=57 .....(4)

Now multiplying equation (4) by 2 such that we will have,

8x-2y=114\ .....(5)8x−2y=114 .....(5)

Now adding equation (3) and (5) we get :

\begin{gathered}13x=234\\\\x=18\end{gathered}

13x=234

x=18

Put x = 18 in equation (4),

\begin{gathered}4(18)-y=57\\\\y=15\end{gathered}

4(18)−y=57

y=15