Answer:
The solution of the system will be: [tex]x= 3[/tex] and [tex]y=-2[/tex]
Step-by-step explanation:
The given system of equations is.......
[tex]3x-2y=13................................(1)\\ \\ 4x+5y=2..................................(2)[/tex]
Multiplying equation (1) by 5 and equation (2) by 2, we will get........
[tex]5(3x-2y)=5(13)\\ 15x-10y=65...............................(3)\\ \\ and\\ \\ 2(4x+5y)=2(2)\\ 8x+10y=4...................................(4)[/tex]
Now, adding equation (3) and (4), we will get.........
[tex](15x-10y)+(8x+10y)=65+4\\ \\ 23x=69\\ \\ x=\frac{69}{23}=3[/tex]
Plugging this [tex]x=3[/tex] into equation (1).........
[tex]3(3)-2y=13\\ \\ 9-2y=13 \\ \\ -2y=4\\ \\ y=\frac{4}{-2}=-2[/tex]
So, the solution of the system will be: [tex]x= 3[/tex] and [tex]y=-2[/tex]
