18Recap

Solution set

$\mathbb{L}=\{(a\mathrm{\mid }b)=(\dots \mathrm{\mid }\dots )\}\backslash mathbb\{L\}=\backslash \{(a|b)=(\dots |\dots )\backslash \}$

Number of solutions

A linear system of equations can have none, one or infinitely many solutions

Elimination by equating coefficients

Step 0: Solve both equations for one variable.

Step 1: Equate the other two sides.

Step 2: Solve for the remaining variable.

Step 3: Insert the obtained value into one of the equations.

Substitution method

Step 1: Solve an equation for one variable.

Step 2: Substitute into the other equation.

Step 3: Substitute the obtained value into one of the equations.

Addition method

Step 0: Clean up the equation and select one variable.

Step 1: Multiply the equations.

Step 2: Remove of the variables.

Step 3: Determine the values.