In 2D, I'll give you that, but in general, I would say "has struggled solving", rather than "has solved", and not even 'everyone'.
Few can, for example, reliably compute the intersection point of a line l' parallel to l through a point p with a plane P, and many would panic when given a problem in N>3-dimensional space.
I know people who memorized formulas for solving linear systems as used in macro-economics (on the order of 10 dimensions, but lots of zeroes in their matrix), and, because of that, couldn't work when given a slightly different model to solve (for example, if taxation became be a constant plus a fraction of income instead of just a fraction of income, or if capital gains tax were introduced).
The first step in a linear algebra course is to codify the method that you use in middle/high school to solve systems of equations of the form a00x0+a01x1+...=b0....
That algorithm sets the stage for everything. The pace is natural, the math is accessible, no geometric interpretation is ever required, and it's built for problems that people of even average intelligence can understand. Frankly, it's astonishing we don't teach it in high school.
Few can, for example, reliably compute the intersection point of a line l' parallel to l through a point p with a plane P, and many would panic when given a problem in N>3-dimensional space.
I know people who memorized formulas for solving linear systems as used in macro-economics (on the order of 10 dimensions, but lots of zeroes in their matrix), and, because of that, couldn't work when given a slightly different model to solve (for example, if taxation became be a constant plus a fraction of income instead of just a fraction of income, or if capital gains tax were introduced).