A set of equations involving the same variables A solution is a collection of values that makes each equation true. Solving a system = finding all solutions Systems of Linear Equations

Substitution Method Pick one equation and solve for one variable in terms of the other. Substitute that expression for the variable in the other equation. Solve the new equation for the single variable and use that value to find the value of the remaining variable.

Elimination Method Multiply both equations by constants so that one variable has coefficients that add to zero. Add the equations together to eliminate that variable. Solve the new equation for the single variable and use that value to find the value of the remaining variable.

Swap the position of two equations Multiply equation by non-zero constant Add a multiple of one equation to another equation Use Left-to-Right Elimination and then Backward Substitution Equivalent Systems of Linear Equations

Example 1

Example 2

Each serving (1 cup) of milk contains 430 mg of potassium and 2.5 g of fat. Each serving (100 g) of peanuts contains 690 mg of potassium and 45 g of fat. If a diet needs to contain 1205 mg of potassium and 27.5 g of fat, then how much of each food is needed? Example 3

Example 3 – continued