Given:
The system of equation is
[tex]15x+12y=18[/tex]
[tex]5x+4y=6[/tex]
To find:
The solution of given system of equations by using elimination method.
Solution:
We have,
[tex]15x+12y=18[/tex] ...(i)
[tex]5x+4y=6[/tex] ...(ii)
Multiply equation (ii) by 3.
[tex]3(5x+4y)=3(6)[/tex]
[tex]3(5x)+3(4y)=18[/tex]
[tex]15x+12y=18[/tex] ...(iii)
After subtracting (iii) from (i), we get
[tex](15x+12y)-(15x+12y)=18-18[/tex]
[tex]15x+12y-15x-12y=0[/tex]
[tex]0=0[/tex]
This statement is true for all values of x and y. So, the given system of equations has infinitely many solutions and both equations represents coincident lines.
