Question

How many solutions does the system have? 2x + 3y = -6 3a - 4y = -12 no solutions O exactly one solution O infinitely many solutions

Answer 1

`\begin{gathered} 2x+3y=-6 \\ 3x-4y=-12 \\ 2x=-6-3y \\ x=-(6)/(2)-(3y)/(2) \\ x=-3-(3)/(2)y \\ 3(-3-(3)/(2)y)-4y=-12 \\ -9-(9y)/(2)-4y=-12 \\ -(9y)/(2)-4y=-12+9 \\ (-9y-8y)/(2)=-3 \\ -(17y)/(2)=-3 \\ -17y=-6 \\ y=(6)/(17) \\ \\ 2x+3((6)/(17))=-6 \\ 2x+(18)/(17)=-6 \\ 2x=-6-(18)/(17) \\ 2x=(-102-18)/(17) \\ 2x=(-120)/(17) \\ 34x=-120 \\ x=-(120)/(34) \\ x=-(60)/(17) \end{gathered}`

Therefore, it has exactly one solution.