We analyzed this standard by parts to better see the content covered. In Part a, we discussed that solutions to a system of two linear equations in two variables correspond to points of intersection of their graph because points of intersection satisfy both equations simultaneously. We used Desmos to visually see where/ if linear equations intersected and showed that the coordinate point of intersection is the x and y values that satisfy each linear equation simultaneously.

In Part b, we solved systems of two linear equations in two variables algebraically. Using the same equations, we found the same solutions without the help of Desmos.  Part c consisted of an example given in grade 8 standard 10. This mathematical problem gave coordinates for two pairs of points, and we had to determine whether the line through the first pair of points intersected the line through the second pair. This process was a bit more challenging since we were not given the equation of the line to determine if the lines intersect. We found the equation of the lines and then determined the point of intersection that satisfied the equations simultaneously.

The implementation of technological and algebraic methods allows for multiple ways of analyzing and solving pairs of simultaneous linear equations. It shows students that there is more than one way to solve linear equations and allows them to choose the way they like best. Teachers may also adapt the examples used when addressing this standard to fit more advanced students. Using multiple methods also engages students which results in the development of a positive mathematical identity. Developing students’ identities should be part of teachers’ daily work, in which they use teaching practices that focus on mathematics, leverage multiple mathematical competencies, affirm mathematical identities, challenge marginality, and draw multiple resources of knowledge (Aguirre, Mayfield- Ingram, and Martin, 2013, as cited in NCTM 2018).

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