Question

Determine if the following system of equations has no solutions , infinitely many solutions or exactly one solution .- Infinitely Many Solutions - One Solution - No Solutions

Answer 1

Let's begin by identifying key information given to us:

$\begin{gathered} x+3y=8----1 \\ x-3y=-6---2 \\ A\text{dd equations 1 \& 2, we have:} \\ x+x+3y-3y=8-6 \\ 2x=2 \\ x=1 \\ \text{Substitute the value of ''x'' into equation 1, we have:} \\ 1+3y=8 \\ \text{Subtract ''1'' from both sides, we have:} \\ 1-1+3y=8-1 \\ 3y=7 \\ y=\frac{7}{3} \end{gathered}$

Therefore, the system of equations has one solution