Solve the following system by graphing. \( x+y-6=0 \) \( x-y=0 \) What is the solution of the system? \( (-3,3) \) \( (3,3) \) \( (3,-3) \)

To solve the system by graphing, we first need to rearrange the equations into slope-intercept form (y = mx + b). For the first equation \( x + y - 6 = 0 \): Rearranging gives us \( y = -x + 6 \). For the second equation \( x - y = 0 \): Rearranging gives us \( y = x \). Now, let's plot both lines. The first line has a negative slope, crossing the y-axis at 6, while the second line is a straight line at a 45-degree angle through the origin. To find the intersection point, we see where these two lines cross. Setting them equal to each other: \(-x + 6 = x\) This simplifies to \(2x = 6\) or \(x = 3\), and substituting back we find \(y = 3\). So, the solution to the system of equations is \( (3, 3) \). For the context, graphing systems of equations is not only a fascinating mathematical skill but also powerful in various fields such as economics, engineering, and physics! When you visualize equations, you get a clear sense of their relationships. And if you ever find yourself graphing complex systems on paper, remember to not rush! A common mistake is misplacing points or miscalculating intersections. Always double-check your graph points and calculations before concluding!