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The point where the lines meet is the point where both equations have a solution. So for Zach’s punch problem, we need to find where the two lines meet. That’s the amount of liquid we want to make the perfect party punch.
Both equations individually have an infinite number of solutions.
Each line is an infinite set of ordered pairs that satisfy that particular equation and make the equation true.
The point where the lines intersect solves the problem.
The intersection is the solution because it solves both equations at the same time. The intersection is a point on both solution lines.