Solve the system of linear equations using Substitution
5x + 2y= 9
y = -x-3

(5, -8)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right  

Distributive Property

Equality Properties

Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of Equality

Algebra I

Terms/CoefficientsCoordinates (x, y)Solving systems of equations using substitution/elimination

Step-by-step explanation:

Step 1: Define Systems

5x + 2y = 9

y = -x - 3

Step 2: Solve for x

Substitution

Substitute in y:                                                                                                 5x + 2(-x - 3) = 9[Distributive Property] Distribute 2:                                                                5x - 2x - 6 = 9Combine like terms:                                                                                        3x - 6 = 9[Addition Property of Equality] Add 6 on both sides:                                   3x = 15[Division Property of Equality] Divide 3 on both sides:                                 x = 5

Step 3: Solve for y

Define original equation:                                                                                y = -x - 3Substitute in x:                                                                                                 y = -5 - 3Subtract:                                                                                                          y = -8