Question

Solve each system of equations by substitution. Clearly identify your solution.

Answer 1

(0, 2)

Explanation:

Since y is x + 2, we can replace y with x + 2

3x + 3y = 6

3x + 3(x+2) = 6

3x + 3x + 6 = 6

6x + 6 = 6

6x = 0

x = 0

y = x + 2

y = 2

Now we can check by replacing x with 0

3x + 3y = 6

3(0) + 3y = 6

0 + 3y = 6

3y = 6

y = 2

Answer 2

(0, 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

Distributive Property

Equality Properties

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

Algebra I

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

Explanation:

Step 1: Define Systems

y = x + 2

3x + 3y = 6

Step 2: Solve for x

Substitution

1. Substitute in y [2nd Equation]: 3x + 3(x + 2) = 6
2. [Distributive Property] Distribute 3: 3x + 3x + 6 = 6
3. Combine like terms: 6x + 6 = 6
4. [Subtraction Property of Equality] Subtract 6 on both sides: 6x = 0
5. [Division Property of Equality] Divide 6 on both sides: x = 0

Step 3: Solve for y

1. Substitute in x [1st Equation]: y = 0 + 2
2. Add: y = 2