Question

if 2x + y = 35 and 3x +4y = 65, find the value of x/y. solve by elimination method​

Answer 1

Answer:

3

Step-by-step explanation:

x = 15 and y = 5

(15, 5)

x / y = 15 ÷ 5 = 3

Answer 2

Given equations

2x + y = 35 .......(i)

3x +4y = 65 ........(ii)

Now,

Let's make the coefficient numerically equal in both equations.

So, on multiplying eq.(i) by 3 and eq.(ii) by 2, we will get,

6x + 3y = 105  ......(iii)

6x + 8y = 130  ......(iv)

On subtracting eq. (iv) from eq.(iii),

   6x +  3y =   105  ......(iii)

(-) 6x (-) 8y = (-)130  ......(iv)

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          -5y  =   -25

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⇒ -5y = -25

⇒ y = (-25) ÷ (-5)

⇒ y = 5

So, the value of y = 5.

Now, by putting the value of y in equation (i), we get

⇒ 2x + (5) = 35

⇒ 2x = 35 - 5

⇒ 2x = 30

⇒ x = 30 ÷ 2

⇒ x = 15

∴ The value of x = 15.

Now, according to the question we have to find the value of

$\bf \frac{x}{y}$

$= \frac{15}{5}$

$= \frac{3}{1}$

$= \boxed{3}$

Hence,

the value of $\boxed{\frac{x}{y} = 3}$

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Verification:

On putting x = 15 and y = 5 in eq.(i) and (ii) respectively, we get,

From eq.(i)

LHS = 2x+y

       = 2(15) + 5

       = 30 + 5

       = 35 = RHS

From eq.(ii)

LHS = 3x + 4y

       = 3(15) + 4(5)

       = 45 + 20

       =  65 = RHS

Hence, the solution is verified.