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FM Substitution

1.3 Simultaneous Linear Equations

Systems of Simultaneous Linear Equations

  • To solve all unknown values in a set of simultaneous linear equations, the number of unknowns must be the same as the number of unique equations in the set.

Number of Solutions for Simultaneous Linear Equations

For two simultaneous linear equations

y=m_{1} x+c_{1}

y=m_{1} x+c_{1}

The number of solutions is defined by the gradient and y-intercept of the two equations.

Unique Solution (m_{1} \neq m_{2})

        • There is a single value for each variable that satisfies every equation.

No Solutions (m_{1} = m_{2}, and c_{1} \neq c_{2})

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