Question

Solve, using the substitution method
j+k=3
j-k=7

Answer 1

k = -2

j = 5

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

• Terms/Coefficients
• Solving systems of equations using substitution/elimination

Explanation:

Step 1: Define Systems

j + k = 3

j - k = 7

Step 2: Rewrite Systems

j - k = 7

1. [Addition Property of Equality] Add k on both sides: j = 7 + k

Step 3: Redefine Systems

j + k = 3

j = 7 + k

Step 4: Solve for k

Substitution

1. Substitute in j [1st Equation]: 7 + k + k = 3
2. [Addition] Combine like terms: 7 + 2k = 3
3. [Subtraction Property of Equality] Subtract 7 on both sides: 2k = -4
4. [Division Property of Equality] Divide 2 on both sides: k = -2

Step 5: Solve for k

1. Substitute in k [1st Equation]: j - 2 = 3
2. [Addition Property of Equality] Add 2 on both sides: j = 5