How many solutions does this system of equations have? x-2y=6 and 3x-6y=18

This system of equations represents two lines in the coordinate system. We can solve for y in both equations to derive their respective slope-intercept form: {eq}x - 2y = 6 Rightarrow y = \frac{1}{2}x - 3{/eq} {eq}3x - 6y = 18 Rightarrow y = \frac{1}{2}x - 3{/eq} Both equations have the same slope of 1/2 and y-intercept of -3, which means they represent the same line. Therefore, there are infinitely many solutions to this system of equations, as any point on the line satisfies both equations.