Answer: The solution to the given system is [tex](x_1,x_2)=(\dfrac{11}{4},\ \dfrac{-3}{4})[/tex]
Step-by-step explanation:
The given system of equations :
[tex]x_1-3x_2=5------------------(1)\\\\ x_1+x_2=2---------------------(2)[/tex]
To solve this , we eliminate equation (1) from (2) , we get
[tex]x_2-(-3x_2)=2-5\ \ [\because (-)(-)=(+)]\\\\\Rightarrow\ x_2+3x_2=-3\\\\\Rightarrow\ 4x_2=-3\\\\\Rightarrow\ x_2=\dfrac{-3}{4}[/tex]
Put value of [tex]x_2[/tex] in (2) , we get
[tex]x_1+(\dfrac{-3}{4})=2[/tex]
[tex]x_1=2-(\dfrac{-3}{4})[/tex]
[tex]x_1=2+\dfrac{3}{4}[/tex] [∵ (-)(-)=(+)]
[tex]x_1=\dfrac{4(2)+3}{4}=\dfrac{11}{4}[/tex]
Hence, the solution to the given system is [tex](x_1,x_2)=(\dfrac{11}{4},\ \dfrac{-3}{4})[/tex]
