Solving Systems of Linear Equations by Elimination Essential Question? How can you solve a system of equations by elimination? 8.EE.8b

Common Core Standard: 8.EE.8 ─ Analyze and solve linear equations and pairs of simultaneous linear equations. b. Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6..

Objectives: To solve a system of linear equations using elimination (linear combinations).

STANDARD FORM of a LINEAR EQUATION In order to use elimination, we must first be able to write an equation in STANDARD FORM with integer coefficients. Remember INTEGER means NO FRACTIONS or DECIMALS Standard form of a Linear Equation looks like: 𝐴𝑥+𝐵𝑦=𝐶 or 𝐴𝑥+𝐵𝑦+𝐶=0

Rewriting in STANDARD FORM Step 1: Eliminate fractions if necessary by multiplying the entire equation by the LCD. Step 2: Move all variable terms to the left and all constant terms to the right. Step 3: Negate all terms (change all signs) if needed to start with a positive leading coefficient.

Rewriting in STANDARD FORM Rewrite in STANDARD FORM: 𝑦=3𝑥−7

Rewriting in STANDARD FORM Rewrite in STANDARD FORM: 𝑦=− 4 3 𝑥+2

Rewriting in STANDARD FORM Rewrite in STANDARD FORM: 5𝑥=2𝑦−11

Rewriting in STANDARD FORM Rewrite in STANDARD FORM: 3 5 𝑦+6= 2 3 𝑥

Graphic Method Algebraic Approaches - Time consuming Substitution solution If a = b , and b = c then a = c. Elimination - Time consuming If a = b and c = d - Not always accurate then a + c = b + d.

ELIMINATION STEPS Step 1: Put the equations in STANDARD FORM. Step 2: Create one set of OPPOSITE COEFFICIENTS. Step 3: ADD the equations and solve.

Solve using elimination. Check!

Solve using elimination. Check!

Solve using elimination. Check!

Solve using elimination. Check!

Solve using elimination. Check!

Solve using elimination. Check!