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Hey @mary-manske
This totally makes sense. I’ve experienced this same issue teaching this same concept. That’s why I teach this lesson to start any linear system topics: http://slamdunkmath.blogspot.com/2013/11/solving-systems-with-manipulatives.html It’s from Alex Overwijk.
I find it helps with students understanding what they are actually finding when solving a linear system.
After that lesson we move to writing equations and then graphing them on Desmos to see that the same solutions can be found by the intersection.
This lesson is also a go to for me: https://teacher.desmos.com/activitybuilder/custom/56d139907e51c4ed1014b51f