Name: Solution of Pair of Linear Equations in 2 Variables
Uploaded: 2019-07-19
Duration: 4 min 6 s
Description: What is the easy way to solve a linear equation in two variables? Which variable should you find out first? Watch the video to know the answer to these quest...

Question

Check each of the given systems of equations to see if it has a unique solution, infinitely many solutions or no solution. Solve them graphically.

$2 x + 3 y = 1 3 x - y = 7$

Accepted Answer

The given equations are $2 x + 3 y = 1 3 x - y = 7$ and $3 x - y = 7$ .

It can be written as $2 x + 3 y - 1 = 0$ and $3 x - y - 7 = 0$ .

Comparing the given equations with standard form $a_{1} x + b_{1} y + c_{1} = 0$ and $a_{2} x + b_{2} y + c_{2} = 0$ , we get,

$a_{1} = 2, b_{1} = 3, c_{1} = - 1$ and $a_{2} = 3, b_{2} = - 1, c_{2} = - 7$

Here, $\frac{a_{1}}{a_{2}} = \frac{2}{3}; \frac{b_{1}}{b_{2}} = \frac{3}{- 1}$ and $\frac{c_{1}}{c_{2}} = \frac{- 1}{- 7} = \frac{1}{7}$

Since $\frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}}$ , therefore they are intersecting lines, and hence, it is a consistent pair of linear equation and has a unique solution.

For the equation $2 x + 3 y = 1$ :

$x$ $y = \frac{1 - 2 x}{3}$ $(x, y)$

$- 1$ $y = \frac{1 - 2 (- 1)}{3} = 1$ $(- 1, 1)$

$2$ $y = \frac{1 - 2 (2)}{3} = - 1$ $(2, - 1)$

For the equation $3 x - y = 7$ :

$x$ $y = 3 x - 7$ $(x, y)$

$2$ $y = 3 (2) - 7 = - 1$ $(2, - 1)$

$3$ $y = 3 (3) - 7 = 2$ $(3, 2)$

The unique solution of this pair of the equation is $(2, - 1)$ .

Telangana Board Solutions for Chapter: Pair of Linear Equations, Exercise 3: Do This

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