Solving Systems of Linear Equations Algebraically Coordinate Algebra w/Lab Coach Adair – CHHS Math
There are 2 fundamental ways of solving a system of 2 linear equations algebraically: using substitution or usingelimination. • To solve a linear system using SUBSTITUTION: • Solve one of the equations for one of its variables. • SUBSTITUTE this representation into the other equation; this creates a new equation with only ONE VARIABLE • Solve the equation. • SUBSTITUTE the solution into other equation and solve. • State the solution…should be an ordered pair .
Example Solve the system below using SUBSTITUTION. Equation 1 (E1) is solved for y in terms of x. Replace the y in Equation 2 (E2) with ; then Solve. Substitute into E1 and Solve. State the solution…
To solve a linear system using ELIMINATION: • Align all “like terms”. • Multiply one or both equations to create “opposites”. • Add the equations to eliminate one of the variables. • Solve the remaining equation. • Substitute the solution into one of the original equations and solve. • State the solution…should be an ordered pair .
Example Solve the system below using ELIMINATION. Multiply Equation 1 by 5 and Equation 2 by 4. Add E1 and E2. Solve. Substitute into E1 and Solve. 9 State the solution….