Question

Frame two linear equations and solve to get the given result. To frame two problems of linear equation in one variable of your choice and solve such that The result of the first problem should be 79 and the next problem is 25.

Answer 1

Linear equations

For the first problem, there is no data given. However a solution is added to help you.

Question: Frame two linear equations and solve to get the result x = 1 and y = 2.

Answer:

Given solution, x = 1 and y = 2

or, 3x = 3 and 4y = 8

Adding 3x = 3 and 4y = 8,

3x + 4y = 11 .....(1)

Adding x = 1 and 4y = 8,

x + 4y = 9 .....(2)

Thus the required linear equations are

3x + 4y = 11, x + 4y = 9 [x = 1, y = 2].

Problem 2.

(i) Given solution is x = 79

Then 2x = 158 and 3x = 237

So, (2x - 158)/5 = 0 and (3x - 237)/7 = 0

We frame the linear equation:

(2x - 158)/5 = (3x - 237)/7

(ii) Given solution is y = 25

Then 7y = 175 or, (7y - 175)/4 = 0

We frame the linear equation:

y - 25 = (7y - 175)/4

Answer 2

Given:

The result of the first problem should be 79 and the next problem is 25.

To find:

Frame two linear equations and solve to get the given result.

Solution:

From given, we have,

The result of the first problem should be 79 and the next problem is 25.

Given the linear system

ax + by = m

cx + dy = n

where a, b, c, d, m, and n are real constants, a pair of numbers x = x0 and y = y0 also written as (x0, y0) is a solution to this system if each equation is satisfied by the pair.  

The set of all such ordered pairs is called the solution set for the system.  

Let us consider, the system of equations to be,

2x + y = 79

2y - x = 25

upon solving these, we get,

x = 133/5 and y = 129/5

We can verify the results by resubstituting the values of x and y in the equations.