Consider this system of linear equations: y = 3/5 x - 2 y = 3/5 x +2

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  1. Without graphing, determine how many solutions you would expect this system of equations to have. Explain your reasoning.
  2. Try solving the system of equations algebraically and describe the result that you get. Does it match your prediction?

Sangeetha Pulapaka

The equations are in the form y = mx + b from. Here m is the slope of the line and b is the y-intercept, which is constant.

  1. The system of linear equations has no solutions. Compare the coefficients of x  (slopes) and the coefficient of the y variables in the given system of linear equations. They are the same, but the constants are different, so the system of linear equations has no solutions.
  2. These equations are in the y = mx + b from. Equating the equations across each other we get \frac{3}{5}x - 2 = \frac{3}{5}x + 2

          \Rightarrow -2 = 2. This is can never be true.

          Since 2\neq -2, this means that there is no solution to these system of linear equations. Yep, it matches my prediction :)

Skills you may want to recall:

What is a y = mx+b form