Question

2^x+3^y=97 and 2^x+2-3y-1=37 then x+y is equal to​

Answer 1

Answer:

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Class 10

>>Maths

>>Pair of Linear Equations in Two Variables

>>Reducing a Pair of Equations to Linear Form

>>Solve: 12(2x + 3y) + 127(3...

Question

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Solve:

2(2x+3y)

1

+

7(3x−2y)

12

=

2

1

and

2x+3y

7

+

3x−2y

4

=2, where 2x+3y



=0 and 3x−2y



=0.

Medium

Solution

verified

Verified by Toppr

Let

2x+3y

1

=u and

3x−2y

1

=v. Then, the given system of equations becomes

2

1

u+

7

12

v=

2

1

⇒7u+24v=7 ..(i)

and, 7u+4v=2 .(ii)

Substracting equation (ii) from equation (i), we get

20v=5⇒v=

4

1

Putting v=

4

1

in equation (i), we get

7u+6=7⇒u=

7

1

Now, u=

7

1

⇒

2x+3y

1

=

7

1

⇒2x+3y=7 (iii)

and, u=

4

1

⇒

3x−2y

1

=

4

1

⇒3x−2y=4 .(iv)

Multiplying equation (iii) by 2 and equation (iv) by 3, we get

4x+6y=14 .(v)

9x−6y=12 .(vi)

Adding equations (v) and (vi), we get

13x=26⇒x=2

Putting x=2 in equation(v), we get

8+6y=14⇒y=1

Hence, x=2,y=1 is the solution of the given system of equal

Answer 2

Answer:

I think you mean to ask 2^x+3^y=97 and 2^(x+2)-3^(y-1)=37 then x+y is equal to.

The value of x + y is 8

Step-by-step explanation:

Given equations are:

$2^{x}+3^{y}=97$

Let it be equation (I)

$2^{(x+2)}-3^{(y-1)}=37$

Let it be equation (II)

From equation (II),

$2^{x}.2^{2}-3^{y}.3^{-1}=37$

$4.2^{x}-\frac{3^{y} }{3}=37$

$12.2^{x}-3^{y}=111$

Let it be equation (III)

By adding equation (I) and(III), we get

$13.2^{x}=208$

$2^{x}=\frac{208}{13}$

$2^{x}=16$

$2^{x}=2^{4}$

x=4

Now putting $2^{x}$ in equation (I), we get

$16+3^{y}=97$

$3^{y}=97-16$

$3^{y}=81$

$3^{y}=3^{4}$

y=4

Now taking the value of x and y in the equation x+ y, we get

x+ y

4+4

8

Hence the value of x+ y is 8.

To solve similar questions refer below,

https://brainly.in/question/4936034

https://brainly.in/question/2559305

Thank you.