Question

Find solution to the system of linear equations. x1 - 3x2 = 5 , x1 + x2 = 2

Answer 1

Answer: The solution to the given system is
`(x_1,x_2)=((11)/(4),\ (-3)/(4))`

Explanation:

The given system of equations :

`x_1-3x_2=5------------------(1)\\\\ x_1+x_2=2---------------------(2)`

To solve this , we eliminate equation (1) from (2) , we get

`x_2-(-3x_2)=2-5\ \ [\because (-)(-)=(+)]\\\\\Rightarrow\ x_2+3x_2=-3\\\\\Rightarrow\ 4x_2=-3\\\\\Rightarrow\ x_2=(-3)/(4)`

Put value of
`x_2` in (2) , we get

`x_1+((-3)/(4))=2`

`x_1=2-((-3)/(4))`

`x_1=2+(3)/(4)` [∵ (-)(-)=(+)]

`x_1=(4(2)+3)/(4)=(11)/(4)`

Hence, the solution to the given system is
`(x_1,x_2)=((11)/(4),\ (-3)/(4))`