Question

Solve the pair of linear equation 29x+41y=169 41x+29y=181

Answer 1

ADDING (i)&(ii) eqn.,
70x + 70y = 350
x + y = 5. ...(iii)

SUBTRACTING (i)&(ii) eqns.
-12x + 12y = -12
x - y = 1. ...(iv)

ADDING (iii)&(iv) eqns.,
2x = 6
x = 3

Therefore, y = 2

HENCE, x=3, y=2

Answer 2

A two-variable linear equation is one with the formula ax+by+c, where a, b, and c are all real numbers and a, b is not equal to zero. In a set of two linear equations in two variables, we deal with two such equations. The answer to such equations is a point on the equation's representational line.

Graphical Approach

The Algebraic Approach

The general formulation of a set of linear equations in two variables, say x and y, is:

$a_1x + b_1y + c_1 = 0$..............(1)

$a_2x + b_2y + c_2 = 0$..............(2)

where $a_1, b_1, c_1, a_2, b_2, c_2, a_{12} + b_{12} = 0$ and $a_{22}+ b_{22} = 0$ are all real values

When the pair of linear equations is written as $a_1x + b_1y + c_1 = 0 and a_2x + b_2y + c_2 = 0$, three conditions apply:

1. An inconsistent pair of linear equations is a set of two linear equations in two variables that has no solution.

2. A consistent pair of linear equations in two variables is a pair of linear equations with a solution.

3. A dependent pair of linear equations is a pair of linear equations in two variables that has an infinite

ADDING (i)&(ii) equation

$70x + 70y = 350$

$x + y = 5$ ...(iii)

SUBTRACTING (i)&(ii) equation

$-12x + 12y = -12$

$x - y = 1$. ...(iv)

ADDING (iii)&(iv) equation

$2x = 6$

$x = 3$

Therefore, $y = 2$

HENCE, $x=3, y=2$

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