Question

Obtain four solutions at equation 4x-y=6.​

Answer 1

Given:

The equation -

• 4x - y = 6

What To Find:

We have to find

• Obtain four solutions for the given equation.

How To Find:

To find it, we have to,

• First, assume any variable either x or y to be a real number.
• Next, substitute the value and solve to find the value of another variable.
• Then, repeated the above steps with another real number till how much the question is asking.
• Finally, find the results of the question.

Solution:

Solution are as follows-

• Case 1:-

Let x be 1.

➨ x = 1

The equation,

➨ 4x - y = 6

Substitute the value of x,

➨ 4 × 1 - y = 6

Multiply 4 with 1,

➨ 1 - y = 6

Take 6 to LHS and y to RHS,

➨ 1 + 6 = y

Add 1 and 6 in LHS,

➨ 7 = y

∴ Hence, the values of x and y are 1 and 7.

• Case 2:-

Let x be 2.

➨ x = 2

The equation,

➨ 4x - y = 6

Substitute the value of x,

➨ 4 × 2 - y = 6

Multiply 4 with 2,

➨ 8 - y = 6

Take 8 to RHS,

➨ - y = 6 - 8

Subtract 8 from 6,

➨ - y = - 2

Cancel the minus sign from both sides,

➨ y =  2

∴ Hence, the values of x and y are 2 and 2.

• Case 3:

Let x be 3.

➨ x = 3

The equation,

➨ 4x - y = 6

Substitute the value of x,

➨ 4 × 3 - y = 6

Multiply 4 with 3,

➨ 12 - y = 6

Take 12 to RHS,

➨ - y = 6 - 12

Subtract 12 from 6,

➨ - y = - 6

Cancel the minus sign from both sides,

➨ y = 6

∴ Hence, the values of x and y are 3 and 6.

• Case 4:

Let x be 4.

➨ x = 4

The equation,

➨ 4x - y = 6

Substitute the value of x,

➨ 4 × 4 - y = 6

Multiply 4 with 4,

➨ 16 - y = 6

Take 16 to RHS,

➨ - y = 6 - 16

Subtract 6 from 16,

➨ - y = - 10

Cancel the minus sign from both sides,

➨ y = 10

∴ Hence, the values of x and y are 4 and 10.

Final Answer:

∴ Hence, the four solutions obtained are as follows -

• (1, 7)
• (2, 2)
• (3, 6)
• (4, 10)