Question

Solve the following pair of linear equations by any algebraic method: 2x + y = 14, x - y = 1.

Answer 1

Given Equations:-

• $\mathtt{2x + y = 14.......(i)}$
• $\mathtt{x - y = 1.......(ii)}$

⠀

Solution:-

$\mathcal \blue{Multiplying\: 2 \: in\: equation\: (ii)}$

$\boxed{We\: get}$

$\mathtt{2x + y = 14}$

$\mathtt{2x - 2y = 2}$

⠀

$\mathcal \green{After\: solving}$

$\mathtt{3y = 12}$

$\mathtt{y = \frac{12}{3}}$

$\mathtt{y = 4}$

⠀

$\mathcal \green{Putting\: the\: value\: of\: y\: in\: equation\: (i)}$

$\mathtt{2x + y = 14}$

$\mathtt{2x + 4 = 14}$

$\mathtt{2x = 10}$

$\mathtt{x = \frac{10}{2}}$

$\mathtt{x = 5}$

___________________

Therefore,

$\large\red{\underline{{\boxed{\textbf{x = 5}}}}}$

$\large\red{\underline{{\boxed{\textbf{y = 4}}}}}$

Answer 2

The given pair of equations are:

11x +15y + 23 = 0 …………………………. (i)

7x – 2y – 20 = 0 …………………………….. (ii)

From (ii)

2y = 7x – 20

⇒ y = (7x −20)/2 ……………………………… (iii)

Now, substituting y in equation (i) we get,

⇒ 11x + 15((7x−20)/2) + 23 = 0

⇒ 11x + (105x − 300)/2 + 23 = 0

⇒ (22x + 105x – 300 + 46) = 0

⇒ 127x – 254 = 0

⇒ x = 2

Next, putting the value of x in the equation (iii) we get,

⇒ y = (7(2) − 20)/2

∴ y= -3

Thus, the value of x and y is found to be 2 and -3 respectively