Math

Systems of Equations

• System 1 vs System 2

  • Some variables missing in System 2 equations.

  • Example:

    • Equation 2 in System 2 lacks 'x', implying the coefficient of 'x' equals 0.

    • Equation 3 in System 2 is missing both 'x' and 'y'.

• Equivalence of Solutions

  • Both Systems have the same solution: (-5, -1, 3).

  • The method used to solve these is backward substitution.

Step-by-Step Solving Process

• Plugging in values:

  • Starting with 'z' set to 3, substitute in the second equation:

    • y + 3 = 2.

    • Solve for 'y':

      • y = -1.

• Finding 'x':

  • Go to the first equation with x and y values:

    • x - 2(-1) = 11.

    • Simplifying gives x = -5.

Conclusion

• The solution (-5, -1, 3) satisfies both System 1 and System 2.

• Verification is straightforward by substituting back into the equations.