Question

Solve using substitution
6x + 7y = - 1
x-y = 15

Answer 1

(8, -7)

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

6x + 7y = -1

x - y = 15

Step 2: Rewrite Systems

x - y = 15

1. [Addition Property of Equality] Isolate x: x = y + 15

Step 3: Solve for y

Substitution

1. Substitute in x [1st Equation]: 6(y + 15) + 7y = -1
2. [Distributive Property] Distribute 6: 6y + 90 + 7y = -1
3. Combine like terms: 13y + 90 = -1
4. [Subtraction Property of Equality] Isolate y term: 13y = -91
5. [Division Property of Equality] Isolate y: y = -7

Step 4: Solve for x

1. Substitute in y [2nd Equation]: x - (-7) = 15
2. Simplify: x + 7 = 15
3. [Subtraction Property of Equality] Isolate x: x = 8