Given :-
- A system of linear equation in two variables .
To Find :-
- The solution set of the system .
Solution :-
The given system of equation is ,
[tex]\begin{cases} 3x + 2y = 9\dots (i) \\\\ y = 4x + 10 \dots (ii)\end{cases}[/tex]
Firstly , taking equation (ii) ,
[tex] y = 4x +10[/tex]
On subtracting y on both sides, we have ;
[tex] 4x - y +10 = 0[/tex]
Multiplying both sides by 2 ,
[tex] 2(4x -y+10)=2(0)[/tex]
Simplify,
[tex] 8x - 2y = -20 \dots (iii)[/tex]
Adding equation (i) and (iii) ,
[tex] 3x + 2y + 8x - 2y = -20+9[/tex]
Add and subtract the like terms ,
[tex] 11x = -11 [/tex]
Divide both sides by 11 ,
[tex] x = -1 [/tex]
Now substitute this value in equation (i) ,
[tex] 3(-1) + 2y = 9\\ \\ -3 + 2y = 9 \\\\ 2y = 9+3 \\\\ 2y = 12 \\\\ y =\dfrac{12}{2}\\\\ y = 6[/tex]
Hence the correct option is 4 (-1,6) .
I hope this helps . Let me know if you need any further clarification .
