Question

Solve by cross multiplication method :-
${\frac{34}{3x+4y}}$+${\frac{15}{3x-2y}}$$=5$
${\frac{25}{3x-2y}}$-${\frac{8.50}{3x+4y}}$$=4.5$​

Answer 1

Hello miraclerb!

We are given two equations:

$\sf \bullet \dfrac{34}{3x+4y} +\dfrac{15}{3x-2y} =5$

$\sf \bullet \dfrac{25}{3x-2y} -\dfrac{8.05}{3x+4y} =4.5$

First, assume:

• 3x – 2y = 1/a
• 3x + 4y = 1/b.

Then we get:

$\sf \bullet 34b+15a =5$

$\sf \bullet 25a -8.05b =4.5$

Now here:

• a₁=15, b₁=34, c₁= -5
• a₂=25, b₂= -8.05, c₂= -4.5

Then:

$\sf \dfrac{a}{b_1 \times c_2-b_2 \times c_1} =\dfrac{b}{c_1 \times a_2-a_1 \times c_2} =\dfrac{-1}{a_1 \times b_2 - b_1 \times a_2}$

Substitute.

$\sf \dfrac{a}{(34 \times -4.5)-(-8.05 \times -5)} =\dfrac{b}{-5 \times 25-(15 \times -4.5)} =\dfrac{-1}{15 \times -8.05 - (34 \times 25)}$

Further solving, we get:

• b=1/17
• a=1/5

Now we assumed:

• 3x – 2y = 1/a
• 3x + 4y = 1/b

Substitute.

• 3x – 2y = 5
• 3x + 4y = 17.

Using elimination method, we finally get:

x=3 and y=2.

The value of x is 3 and y is 2.

Answer 2

Answer:

We are given two equations:

\sf \bullet \dfrac{34}{3x+4y} +\dfrac{15}{3x-2y} =5∙

3x+4y34 +3x−2y15 =5

\sf \bullet \dfrac{25}{3x-2y} -\dfrac{8.05}{3x+4y} =4.5∙

3x−2y

25 − 3x+4y8.05=4.5

First, assume:

3x – 2y = 1/a

3x + 4y = 1/b.

Then we get:

\sf \bullet 34b+15a =5∙34b+15a=5

\sf \bullet 25a -8.05b =4.5∙25a−8.05b=4.5

Now here:

a₁=15, b₁=34, c₁= -5

a₂=25, b₂= -8.05, c₂= -4.5

Then:

\sf \dfrac{a}{b_1 \times c_2-b_2 \times c_1} =\dfrac{b}{c_1 \times a_2-a_1 \times c_2} =\dfrac{-1}{a_1 \times b_2 - b_1 \times a_2}

b

1 ×c 2 −b 2 ×c 1a

= c1 ×a 2 −a1×c 2b

= a 1 ×b 2 −b 1×a 2−1

Substitute.

\sf \dfrac{a}{(34 \times -4.5)-(-8.05 \times -5)} =\dfrac{b}{-5 \times 25-(15 \times -4.5)} =\dfrac{-1}{15 \times -8.05 - (34 \times 25)}

(34×−4.5)−(−8.05×−5)

a

=

−5×25−(15×−4.5)b

= 15×−8.05−(34×25)−1

Further solving, we get:

b=1/17

a=1/5

Now we assumed:

3x – 2y = 1/a

3x + 4y = 1/b

Substitute.

3x – 2y = 5

3x + 4y = 17.

Using elimination method, we finally get:

x=3 and y=2.

The value of x is 3 and y is 2