Question

What is the solution to the system of equations shown below?

2x + 2y = 12
6x - 2y = 20

A (0,6) B (2, 2) C (3,3) D (4,2)​

Answer 1

D (4, 2)

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

Equality Properties

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

Algebra I

• Coordinates (x, y)
• Solving systems of equations using substitution/elimination

Explanation:

Step 1: Define Systems

2x + 2y = 12

6x - 2y = 20

Step 2: Solve for x

Elimination

1. Combine 2 equations: 8x = 32
2. [Division Property of Equality] Divide 8 on both sides: x = 4

Step 3: Solve for y

1. Define original equation: 2x + 2y = 12
2. Substitute in x: 2(4) + 2y = 12
3. Multiply: 8 + 2y = 12
4. [Subtraction Property of Equality] Subtract 8 on both sides: 2y = 4
5. [Division Property of Equality] Divide 2 on both sides: y = 2