Question

:- Write down the two statements of Linear equations

in two variables in your daily life. Draw their graph. Verifying

the conditions of consistency / inconsistency.​

Answer 1

Step-by-step explanation:

Given:Write down the two statements of Linear equations in two variables in your daily life.

To find:Draw their graph. Verifying

the conditions of consistency / inconsistency.

Solution:As we have to construct a word problem such that it form simultaneous linear equation in two variable, it can be like that

Problem: If twice the age of Aditi is added to age of her father, the sum is 56. But if twice the age of the father is added to the age of Aditi, the sum is 82. Find the ages of Aditi and her father.

Step 1: Formation of linear equations

Let the age of Aditi's father is x years

and Aditi's age is y years

according to the question

$x+2y = 56 \: \: \: eq1 \\ \\ 2x + y = 82 \: \: \: eq2$

Step 2: Check condition of consistency

If

$a_1x + b_1y + c_1 = 0 \\ \\ a_2x + b_2y + c_2 = 0$

Then equations are consistent if

$\boxed{\frac{a_1}{a_2} \neq \frac{b_1}{b_2}}$

Check consistency for eq1 and eq2

$\frac{1}{2} \neq \frac{2}{1}$

Thus, equations formed by the word problem are consistent and having a unique solution.

Step 3: Solution of linear equations using algebraic method.

$x = 56 - 2y \: \: \: in \: eq \: 2 \\ \\ 2(56 - 2y) = 82 \\ \\ - 4y + y = 82 - 112 \\ \\ 3y = 30 \\ \\ y = 10$

So,

$\begin{gathered}2(10) + x = 56 \\ \\ x = 56 - 20 \\ \\ x = 36 \\ \end{gathered}$

So,

Aditi's age is 10 years and Aditi's father age is 36 years.

Step 4: Draw graph of equation

x+2y=56

put x=0,y=56/2=28; (0,28)

put y=0,x=56;(56,0)

2x+y=82

put x=0,y=82;(0,82)

put y=0,x=82/2=41;(41,0)

Mark these points and join them.Both lines cut at one place;which is solution of equations.

Graph is attatched and solution using graphical method too was shown.

Note*:Ignore the graph in II and IV quadrant; because age of person never be negative.But length of line is infinite thus it crosses both mentioned quadrants.

Hope it helps you.

To learn more on brainly:

solve the following system of linear equation graphically: 3x+y-11=0 and x-y-1=0

shade the region bounded by these lines...

https://brainly.in/question/3050092

Answer 2

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