SECTION 3.2 SOLVING LINEAR SYSTEMS ALGEBRAICALLY Advanced Algebra Notes

Solving Linear Systems Algebraically In this lesson, we will study two algebraic methods for solving linear systems. The first method is called the Substitution method

USING THE SUBSTITUION METHOD Solve one of the equations for one of its variables, x or y Substitute the expression from Step 1 in the other equation & solve for the other variable Substitute the value from Step 2 in the revised equation from Step 1 and solve

Example 1

USING THE ELIMINATION METHOD Multiply one or both of the equations by a to obtain coefficients that differ only in sign for one of the variables Combine “Like Terms” in the revised equations one of our variables should be eliminated solve for the remaining variable. Substitute the variable solved for into either of the ORIGINAL equations to solve for the remaining variable

Example 2

Example 3

Solve the linear system 4x-10y=8 -14x+35y=-28 Example 4

Closing: How do you solve a system of linear equations algebraically? Elimination Method Substitution Method Multiplying by a factor to obtain opposites Plugging in a variable that has a coefficient of 1 Using the: Solve for one variable. Then plug back in to find the second. WRITE YOUR ANSWER AS A COORDINATE POINT HW: #