Question

solve by criss cross

3x+y=13

x-3y+9=0

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Answer 1

Appropriate Question :-

Solve the following by Cross Multiplication method

• 3x + y = 13

• x - 3y + 9 = 0

$\large\underline{\sf{Solution-}}$

The above equation are

$\rm :\longmapsto\:3x + y = 13$

and

$\rm :\longmapsto\:x - 3y = - 9$

Using cross multiplication method, we have

$\begin{gathered}\boxed{\begin{array}{c|c|c|c} \bf 2 & \bf 3 & \bf 1& \bf 2\\ \frac{\qquad}{} & \frac{\qquad}{}\frac{\qquad}{} &\frac{\qquad}{} & \frac{\qquad}{} &\\ \sf 1 & \sf 13 & \sf 3 & \sf 1\\ \\ \sf - 3 & \sf - 9 & \sf 1 & \sf - 3\\ \end{array}} \\ \end{gathered}$

So,

$\rm :\longmapsto\:\dfrac{x}{ - 9 - ( - 39)} = \dfrac{y}{13 - ( - 27)} = \dfrac{ - 1}{ - 9 - 1}$

$\rm :\longmapsto\:\dfrac{x}{ - 9 + 39} = \dfrac{y}{13 + 27} = \dfrac{ - 1}{ - 10}$

$\rm :\longmapsto\:\dfrac{x}{30} = \dfrac{y}{40} = \dfrac{1}{10}$

On multiply by 10, we get

$\rm :\longmapsto\:\dfrac{x}{3} = \dfrac{y}{4} = \dfrac{1}{1}$

Now, taking first and third member, we get

$\rm :\longmapsto\:\dfrac{x}{3} = \dfrac{1}{1}$

$\bf\implies \:x = 3$

Now, taking second and third member, we get

$\rm :\longmapsto\: \dfrac{y}{4} = \dfrac{1}{1}$

$\bf\implies \:y = 4$

$\begin{gathered}\begin{gathered}\bf\: \rm :\longmapsto\:Hence-\begin{cases} &\sf{x = 3} \\ &\sf{y = 4} \end{cases}\end{gathered}\end{gathered}$

Verification :-

Consider equation (1), we have

$\rm :\longmapsto\:3x + y = 13$

Put x = 3 and y = 4

$\rm :\longmapsto\:3 \times 3 + 4 = 13$

$\rm :\longmapsto\:9 + 4 = 13$

$\rm :\longmapsto\:13 = 13$

Hence, verified.

Consider equation (2), we have

$\rm :\longmapsto\:x - 3y = - 9$

Put x = 3 and y = 4, we get

$\rm :\longmapsto\:3 - 3 \times 4 = - 9$

$\rm :\longmapsto\:3 - 12 = - 9$

$\rm :\longmapsto\: - 9 = - 9$

Hence, Verified.

Answer 2

Answer:

3x + y = 13 ———— (i)

x – 3y + 9 = 0

x – 3y = – 9 ———— (ii)

if we into this, (i)×1 and (ii)×3

so, 3x+y=13

3x-9y= - 27

(–) (+) (+)

______________

10y = 40

so, the value of y = 4

we put no. (i) equation y =4,

3x + 4 = 13

=> 3x = 13 – 4

=> 3x = 9

=> x = 3

so, the value of x = 3 &

y = 4 ans.

Step-by-step explanation:

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