Question

if 4x+6y=15 and 6x-8y = 14 then find the value of 3x-2y
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Answer 1

Given, a pair of linear equations in two variable:-

4x+6y= 15 ------ (1)

6x-8y = 14 ----- (2)

LCM (4,6) = 12

I.e, (1) × 3 ==> 12x + 18y = 45 ----- (3)

(2) × 2 ==> 12x - 16y = 28 ---- (4)

(3) - (4) ==> 34y = 17

y = 17/34

y = 1/2

So, in (1), 4x - 6(1/2) = 15

---> x = (15 - 3)/4

---> x = 12/4

---> x = 3

Since, we have found x and y, let's find the value of 3x - 2y

==> 3(3) - 2(1/2)

--> 9 - 1

--> 8

∴ 3x - 2y = 8

Note: I have solved the equations using Elimination Method. You can also do it by Substitution Method or Cross Multiplication. :)

Answer 2

3x-2y=8

Given:

• Two linear equations $4x + 6y = 15$ and $6x - 8y = 14$.

To find:

• Find the value of 3x-2y.

Solution:

Concept to be used:

• Using the elimination method, find the values of x and y, hence find 3x-2y.

Step 1:

Multiply eq1 by 8 and eq2 by 6 and add both equations.

$4x + 6y = 15...eq1$

$6x - 8y = 14...eq2$

$32x + 48y = 120 \\ 36x - 48y = 84 \\ - - - - - - - - \\ 68x = 204 \\ - - - - - - - -$

or

$x = \frac{204}{68}$

$\bf x = 3$

Step 2:

Calculate the value of y.

$4x + 6y = 15$

$12 + 6y = 15$

$6y = 3$

$\bf y = \frac{1}{2}$

Step 3:

Find the value of 3x-2y.

Put the value of x and y from step 1 and step 2.

$3x - 2y = 3 \times 3 - 2 \times \frac{1}{2}$

$= 9 - 1$

$\bf 3x - 2y = 8$

Thus,

Value of 3x-2y is 8.

Learn more:

1) Solve the following pair of equations 2x + 5y = 3 and 7x – 2y = 4 by elimination method

https://brainly.in/question/18595258

2) Solution of simultaneous linear equation 2x/y-y/2 =-1/6 and x/2+2y/3 =3

https://brainly.in/question/18702464

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