Question

I need some question of liner Equation in any veriable
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Answer 1

Answer:

☺fg6ugct6Wzdct8ucc7g8g

Step-by-step explanation:

y yv ob0uv9yg

Answer 2

Answer:

Using the method of substitution to solve the pair of linear equation, we have:

2x + 5y = 20…………………….(i)

3x+6y =12……………………..(ii)

Multiplying equation (i) by 3 and (ii) by 2, we have:

6x + 15y = 60…………………….(iii)

6x+12y = 24……………………..(iv)

Subtracting equation (iv) from (iii)

3y = 36

⇒ y = 12

Substituting the value of y in any of the equation (i) or (ii), we have

2x + 5(12) = 20

⇒ x = −20

Therefore, x=-20 and y =12 is the point where the given equations intersect.

Now, it is important to know the situational examples which are also known as word problems from linear equations in 2 variables.

Check: Linear Equations Calculator

Word Problems

Question 1: A boat running downstream covers a distance of 20 km in 2 hours while for covering the same distance upstream, it takes 5 hours. What is the speed of the boat in still water?

Solution:

These types of questions are the real-time example of linear equations in two variables.

In water, the direction along the stream is called downstream. And, the direction against the stream is called upstream.

Let us consider the speed of a boat is u km/h and the speed of the stream is v km/h, then:

Speed Downstream = (u + v) km/h

Speed Upstream = (u – v) km/h

We know that Speed = Distance/Time

So, the speed of boat when running downstream = (20⁄2) km/h = 10 km/h

The speed of boat when running upstream = (20⁄5) km/h = 4 km/h

From above, u + v = 10>…….(1)

u – v = 4 ………. (2)

Adding equation 1 and 2, we get: 2u = 1

u = 7 km/h

Also, v = 3 km/h

Therefore, the speed of the boat in still water = u = 7 km/h

Question 2: A boat running upstream takes 6 hours 30 minutes to cover a certain distance, while it takes 3 hours to cover the same distance running downstream. What is the ratio between the speed of the boat and speed of the water current respectively?

Solution: If the speed downstream is a km/hr and the speed upstream is b km/hr, then

Speed in still water = a + b km/h

Rate of stream = ½ (a − b) kmph

Let the Boat’s rate upstream be x kmph and that downstream be y kmph.

Then, distance covered upstream in 6 hrs 30 min = Distance covered downstream in 3 hrs.

⇒ x × 6.5 hrs = y × 3hrs

⇒ 13/2x = 3y

⇒ y = 13x/6

The required ratio is = y+x2 : y–x2 ⇒ 13x6 + x2 : 13x6 − x2 ⇒ 19x62 : 7x62

= 19:7

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