Question

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

Answer 1

x = - 3

y = 5

Explanation:

y = x + 8 ------(I)

x + y = 2 -------------(II)

Substitute y = x + 8 in equation (II)

x + x + 8 = 2

Combine like terms

2x + 8 = 2

Subtract r from both sides

2x = 2- 8

2x = -6

Divide both sides by 2

x = -6/2

x = -3

Plug in x = -3 in equation (I)

y = -3 + 8

y = 5

Answer 2

(-3, 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

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

Explanation:

Step 1: Define Systems

y = x + 8

x + y = 2

Step 2: Solve for x

Substitution

1. Substitute in y [2nd Equation]: x + x + 8 = 2
2. Combine like terms: 2x + 8 = 2
3. [Subtraction Property of Equality] Subtract 8 on both sides: 2x = -6
4. [Division Property of Equality] Divide 2 on both sides: x = -3

Step 3: Solve for y

1. Substitute in x [1st Equation]: y = -3 + 8
2. Add: y = 5