Question

Solve the following simultaneous equations. 7 (b) 4x + 3/y = 9 3x + 6/y = 8​

Answer 1

Given Equation

4x + 3/y = 9 (i)

3x + 6/y = 8 (ii)

To find the value of x and y

Now let 1/y = u , we get

4x + 3u = 9 (iii)

3x + 6u = 8 (iv)

Now Using Substitution Method , So Take (i)eq

4x + 3u = 9

4x = 9 - 3u

x = (9 - 3u)/4 (v)

Put the value of x on (iv)

3(9 - 3u)/4 + 6u = 8

By taking LCM we get

3(9 - 3u ) + 24u = 8×4

27 - 9u + 24u = 32

15u = 32 - 27

15u = 5

u = 5/15

u = 1/3

Now put the value of u on (v)

x = (9 - 3u)/4 (v)

x = (9 - 3×1/3)/4

x = (9 - 1)/4

x = 8/4

x = 2

If u = 1/3 then y is

1/y = 1/3

y = 3

Answer

x = 2 and y = 3

Answer 2

Step-by-step explanation:

$\\ \qquad\quad\sf{:}\longrightarrow 4x+3/y=9\dots(1)$

$\\ \qquad\quad\sf{:}\longrightarrow 3x+6/y=8\dots(2)$

Let

x=u and 1/y=v

$\\ \qquad\quad\sf{:}\longrightarrow 4u+3v=9\dots(3)$

$\\ \qquad\quad\sf{:}\longrightarrow 3u+6v=8$

Lets use substitution

• From eq(3)

$\\ \qquad\quad\sf{:}\longrightarrow 4u+3v=9$

$\\ \qquad\quad\sf{:}\longrightarrow 4u=9-3v$

$\\ \qquad\quad\sf{:}\longrightarrow u=\dfrac{9-3v}{4}\dots(5)$

• put the value in eq(4)

$\\ \qquad\quad\sf{:}\longrightarrow 3(\dfrac{9-3v}{4})+6v=8$

$\\ \qquad\quad\sf{:}\longrightarrow 27-9v/4+6v=8$

$\\ \qquad\quad\sf{:}\longrightarrow \dfrac{27-9v+24v}{4}=8$

$\\ \qquad\quad\sf{:}\longrightarrow 27+15v=32$

$\\ \qquad\quad\sf{:}\longrightarrow 15v=32-27=5$

$\\ \qquad\quad\bf{:}\longrightarrow v=5/15=1/3$

• Substitute the value in eq(5)

$\\ \qquad\quad\sf{:}\longrightarrow u=9-3(1/3)/4$

$\\ \qquad\quad\sf{:}\longrightarrow 9-1/4$

$\\ \qquad\quad\sf{:}\longrightarrow 8/4$

$\\ \qquad\quad\bf{:}\longrightarrow u=2$

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$\\ \qquad\quad\bf{:}\longrightarrow x=u=2$

$\\ \qquad\quad\sf{:}\longrightarrow 1/y=v=1/3$

$\\ \qquad\quad\sf{:}\longrightarrow y=3$

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$\\ \\ \therefore\sf (x,y)=(2,3)$