Question

1. Solve for x and y: 49x + 51y = 149 and 51x +49y = 151​

Answer 1

$\sf\huge\bold{\underline{\underline{{Solution}}}}$

The above question can be solve through various ways like elimination method , substitution method and cross multiplication method.

We will solve it through cross multiplication method.

49x+51y=149----(1)

51x+49y=151-----(2)

General form of cross multiplication method:

$\sf \boxed{\bold{ \dfrac{x}{b_{1}c_{2} - b_{2}c_{1}} = \dfrac{ - y}{c_{1}a_{2} - c_{2}a_{1}} = \dfrac{1}{a_{1}b_{2} - a_{2}b_{1}} }}$

$\sf \longmapsto \dfrac{x}{51 \times 151 - 49 \times 149} = \dfrac{ - y}{149 \times 51 - 151 \times 49} = \dfrac{1}{49 \times 49 - 51 \times 51}$

$\sf \longmapsto \dfrac{x}{7701 - 7301} = \dfrac{ - y}{7599 - 7399} = \dfrac{1}{2401 - 2601}$

$\sf \longmapsto \dfrac{x}{400} = \dfrac{ - y}{200} = \dfrac{1}{ - 200}$

$\sf \longmapsto \dfrac{ - y}{200} = \dfrac{1}{ - 200}$

$\sf \longmapsto - 200 \times - y = 200$

$\sf \longmapsto200y = 200$

$\sf \longmapsto \: y = 1$

Now ,put y's value into equation 1

=>49x+51=149

=>49x=98

=>x=98÷49=2

=>x=2

∴x=2 & y=1

Check

=>49x+51y=149

=>49×2+51

=>98+51

=>149

LHS=RHS(verified)

Answer 2

51x+49y=150...(1)

49x+51y=50...(2)

Adding eq (1) & (2)

100x+100y=200

x+y=2...(3)

Subtracting eqn (2) from (1)

2x−2y=100

x−y=50...(4)

Adding eqn (3) & (4)

x+y=2

x−y=50

_______________

2x=52

x=26

x+y=2

26+y=2

y=−24

finding x−y & x+y

i.e from (3) & (4)

x−y:x+y⇒50:2

⇒25:1