Determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution. -2x+y=-3 6x-3y=7 Answer No Solutions Infinitely Many Solutions One Solution

## Step 1: Convert to Slope-Intercept Form<br />### Convert both equations to the form $y = mx + b$ to identify slopes and intercepts.<br />- For the first equation $-2x + y = -3$, solve for $y$: <br /> \[<br /> y = 2x - 3<br /> \]<br /> The slope is $2$.<br /><br />- For the second equation $6x - 3y = 7$, solve for $y$: <br /> \[<br /> -3y = -6x + 7 \implies y = 2x - \frac{7}{3}<br /> \]<br /> The slope is also $2$.<br /><br />## Step 2: Compare Slopes and Intercepts<br />### Compare the slopes and $y$-intercepts of both equations to determine the number of solutions.<br />- Both equations have the same slope ($m = 2$), indicating they are parallel.<br />- The $y$-intercepts are different: $-3$ for the first equation and $-\frac{7}{3}$ for the second equation.<br /><br />Since the lines are parallel and have different $y$-intercepts, they do not intersect.