Question

find the ratio x:y:z from 2x+3y-5z=0 and -3x+2y+7z=0 ​

Answer 1

Answer:

2x+3y-5z=0....[x3]

-3x+2y+7z=0....[x2]

6x+9y=15z

-6x +4y=-14z

13y=1z

y:z=13:1

6x+9y=15z

6x+9[1/13]=15[13]

6x+9/13=195

x=32.43

Answer 2

Answer:

The required ratio is $31:1:13$

Step-by-step explanation:

Step 1 of 3

Consider the equations as follows:

$2x+3y-5z=0$ . . . . . (1)

$-3x+2y+7z=0$ . . . . . (2)

Multiply the equation (1) by the number $3$, we get

$3\times (2x+3y-5z)=3\times0$

$6x+9y-15z=0$ . . . . . (3)

Multiply the equation (2) by the number $2$, we get

$2\times(-3x+2y+7z)=2\times0$

$-6x+4y+14z=0$ . . . . . (4)

Subtracting equation (3) and (4) as follows:

$6x+9y-15z-6x+4y+14z=0$

Simplify as follows:

⇒ $9y-15z+4y+14z=0$

⇒ $13y-z=0$

Computing the ratio of $y$ to $z$.

⇒ $13y=z$

⇒ $\frac{y}{z}=\frac{1}{13}$

Thus, ratio of $y$ to $z$ is $1:13$.

Step 2 of 3

Find the ratio of $x$ to $y$.

Substitute the value $z=13y$ in the equation (1) as follows:

⇒ $2x+3y-5(13y)=0$

⇒ $2x+3y-65y=0$

⇒ $2x-62y=0$

⇒ $2x=62y$

⇒ $\frac{x}{y} =\frac{31}{1}$

Thus, ratio of $x$ to $y$ is $31:1$.

Step 3 of 3

Ratio of $x:y:z$.

Since ratio of $x$ to $y$ is,

$x:y=31:1$ . . . . . (i)

And ratio of $y$ to $z$ is,

$y:z=1:13$ . . . . . (ii)

From (i) and (ii), we get

$x:y:z=31:1:13$.

Therefore, the ratio of $x:y:z$ is $31:1:13$.

#SPJ2