Question

1. Show that the following system of equations has a unique solution
3x + 5y = 12,5x + 3y = 4.
Also, find the solution of the given system of equations,unique solution​

Answer 1

Answer:

3x+5y=125x+3y=4

3x+125x=5y+3y=4

128x=8y=4 = Answer

Step-by-step explanation:

Answer 2

Answer:

The given system of equations is: 3x + 5y = 12

5x + 3y = 4

These equations are of the forms: a1x+b1y+c1 = 0 and a2x+b2y+c2 = 0

where, a1 = 3, b1= 5, c1 = -12 and a2 = 5, b2 = 3, c2 = -4

For a unique solution, we must have ,

a1/a2 not equal b1/b2 ., 3/5 not equal 5/3

Hence, the given system of equations has a unique solution.

Again, the given equations are:

3x + 5y = 12 …..(i)

5x + 3y = 4 …..(ii)

On multiplying (i) by 3 and (ii) by 5, we get:

9x + 15y = 36 …….(iii)

25x + 15y = 20 ……(iv)

On subtracting (iii) from (iv), we get:

16x = -16

⇒x = -1

On substituting x = -1 in (i), we get

: 3(-1) + 5y = 12

⇒5y = (12 + 3) = 15

⇒y = 3

Hence, x = -1 and y = 3 is the required solution.