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Linear equations

What are linear equations?

  • Linear equations contain variables to a power of one. For example, variables could be \(x\) and \(y\) but not \(x^{2}\) or \(y^{3}\).
  • They do not contain products of variables. For example, \(xy\,,\ yz\,,\ xyz\)  are not allowed.
  • Examples of linear and nonlinear equations:
    • \(x + 2 = 5\) is a linear equation
    • \(3x - 4y = -1\) is a linear equation
    • \(x^{2} + 2 = 5\) is a nonlinear equation
    • \(xy + 3 = 7\) is a nonlinear equation
  • The most commonly used is the linear equation for a straight line \[y=mx+c\] where \(m\) is the slope or gradient of the line and \(c\) is the \(y\)-intercept.

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