- Step 1: Simplify the equations Simplify the equations by combining like terms and evaluating expressions in parentheses.
- Step 2: Rewrite an equation Rewrite one of the equations as an expression involving a single variable.
- TIP: Given the equations 5x plus 3y equals 38 and 7x minus 3y equals 46, rewrite the second one as y equals (7x minus 46) divided by 3.
- Step 3: Substitute the isolated variable Substitute the isolated variable in the other equation.
- TIP: Substituting for y, the equation 5x plus 3y equals 38 becomes 5x plus 7x minus 46 equals 38.
- Step 4: Solve the equation in one variable Solve for the remaining variable, then go back and calculate the value of the first one.
- TIP: Solving 5x plus 7x minus 46 equals 38, gives x equals 7. Since y equals (7x minus 46) / 3, y must equal 1.
- Step 5: Solve larger systems of equations analogously Use an analogous procedure to solve systems of equations involving larger numbers of variables.
- FACT: Babylonian mathematicians were probably the first to solve linear algebraic equations in more than one variable.
You Will Need
- A set of algebraic equations
- A pencil and paper
- A calculator