Question

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

Answer 1

(5, -8)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

1. Brackets
2. Parenthesis
3. Exponents
4. Multiplication
5. Division
6. Addition
7. 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/Coefficients
• Coordinates (x, y)
• Solving systems of equations using substitution/elimination

Explanation:

Step 1: Define Systems

5x + 2y = 9

y = -x - 3

Step 2: Solve for x

Substitution

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

Step 3: Solve for y

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