Question

How many solutions will you get for :-
$\sf2x + y = 6$
​

Answer 1

Given :-

How many solutions will you get for :-

$\sf2x + y = 6$

Solution :-

There must be four solutions for the given Equation :-

1st Solution :-

Let's assume,

x = 2

y = 2

As,

2*2 + 2 = 6

4 + 2 = 6

6 = 6

LHS = RHS

2nd Method :-

Let's assume,

x = 1

y = 4

As,

2*1 + 4 = 6

2 + 4 = 6

6 = 6

LHS = RHS

3rd Method :-

Let's assume,

x = 3

y = 0

As,

2*3 + 0 = 6

6 + 0 = 6

6 = 6

LHS = RHS

4th Method :-

Let's assume,

x = 0

y = 6

As,

2*0 + 6 = 6

0 + 6 = 6

6 = 6

LHS = RHS

Thank You*

Answer 2

Given:–

• 2x + y = 6

To Find:–

• How many solutions will satisfy above equation ?

Solution:–

❐ Taking the value of 'x' be 0

$\rm{\implies 2(0) + y = 6}$

$\large\implies{\bf{\underline{\red{\: \: y = 6\: \:}}}}$

∴ The solution of the equation is (0, 6)

❐ Now Putting x = 1, we get

$\rm{\implies 2(1) + y = 6}$

$\rm{\implies 2 + y = 6}$

$\rm{\implies y = 6-2}$

$\large\implies{\bf{\underline{\red{ \: \:y = 4\: \:}}}}$

∴ The solution of the equation is (1,4)

❐ Now, Putting x = 2, We get

$\rm{\implies 2(2) + y = 6}$

$\rm{\implies 4 + y = 6}$

$\rm{\implies y = 6-4}$

$\large\implies{\bf{\underline{\red{\: \: y = 2\: \:}}}}$

∴ The solution of the equation is (2,2)

❐ Now, Put 3 at the place of 'x'

$\rm{\implies 2(3) + y = 6}$

$\rm{\implies 6 + y = 6}$

$\rm{\implies y = 6-6}$

$\large\implies{\bf{\underline{\red{ \: \: y = 0 \: \:}}}}$

∴ The solution of the equation is (3,0)

There are Infinite Solutions of this equation, But they contain negative values.

❝ Hence, there are 4 solutions having postive values are (0,6), (1,4), (2,2), (3,0) ❞

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