Question

Find the roots of equation 4x+3y=12

Answer 1

Question :- find the roots of the equation 4x + 3y = 12 ?

Solution :-

we know that,

• Root of an equation definition are values which, substituted for the unknown quantity in an equation, satisfies the equation.

So, given equation is :-

• 4x + 3y = 12 .

we will try to put values one by one .

1) putting x = 0

→ 4x + 3y = 12

→ 4 * 0 + 3y = 12

→ 0 + 3y = 12

→ 3y = 12

dividing both sides by 3,

→ y = 4.

Therefore, roots of equation are (0 , 4).

2) putting y = 0

→ 4x + 3y = 12

→ 4x + 3 * 0 = 12

→ 4x + 0 = 12

→ 4x = 12

dividing both sides by 4,

→ x = 3.

Therefore, roots of equation are (3 , 0).

3) putting x = 1

→ 4x + 3y = 12

→ 4 * 1 + 3y = 12

→ 4 + 3y = 12

→ 3y = 12 - 4

→ 3y = 8

dividing both sides by 3,

→ y = (8/3) .

Therefore, roots of equation are (1 , 8/3).

4) putting y = 1

→ 4x + 3y = 12

→ 4x + 3 * 1 = 12

→ 4x + 3 = 12

→ 4x = 12 - 3

→ 4x = 9

dividing both sides by 4,

→ x = (9/4) .

Therefore, roots of equation are (9/4 , 1).

Hence, we can conclude that, roots of the given linear equation are (0 , 4) , (3, 0) , (1, 8/3) and (9/4 , 1).

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Answer 2

SOLUTION :

TO DETERMINE

The roots of equation 4x + 3y = 12

CONCEPT TO BE IMPLEMENTED

LINEAR EQUATION

A linear equation is an algebraic equation consisting of variables and constants and equality sign in which each term has an exponent of one

REASON BEHIND THE NAME

If you plot the solutions of a linear equation in Cartesian Coordinate system the results in a straight line.

EVALUATION

$\sf{}The \: given \: equation \: is \: \: 4x + 3y = 12$

SOLUTION IN THE SET OF NATURAL NUMBERS

In the set of natural numbers there is no solution

SOLUTION IN THE SET OF WHOLE NUMBERS

In the set of whole numbers there are finite number of solutions

The solutions are (3,0),(0,4)

SOLUTION IN THE SET OF NATURAL NUMBERS

In the set of Real numbers there are infinite number solutions

For example The solutions are

$\displaystyle \sf{}(3,0),(0,4), \bigg( \frac{3}{2} ,2 \bigg), \bigg( 2 , \frac{4}{3} \bigg) \: \:........$

More precisely any point on the line 4x + 3y = 12 is a solution of the equation under set of Real numbers

━━━━━━━━━━━━━━━━

LEARN MORE FROM BRAINLY

Draw the graph of the linear equation

2 x + 3 y = 12.

At what points, the graph of the equation cuts the X & Y axes?

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