Question

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

Answer 1

The system has no solution.

Explanation:

y = 2x + 1

2x - y = 3

• substitute the given value of y into the equation 2x - y = 3.

2x - ( 2x +1) = 3

• Distribute minus sign.

2x - 2x + 1 = 3

• Combine like terms.

1 ≠ 3

Since system has no solution for x, the system has no solution.

Answer 2

No solutions.

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 = 2x + 1

2x - y = 3

Step 2: Solve for x

Substitution

1. Substitute in y [2nd Equation]: 2x - (2x + 1) = 3
2. [Distributive Property] Distribute negative: 2x - 2x + 1 = 3
3. Combine like terms: 1 ≠ 3