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7. Systems of Equations: Know what you d... > The INTERSECTION of the lines solves...

The INTERSECTION of the lines solves BOTH linear equations

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.

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  • 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.

Sharpen your pencil

Check the solution point (4, 1) in both equations to see if it works. Is our solution right?


  

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