Question

Which is the solution to the system of equations?

4x + 2y = -1
3x + 4y = 3

A. (0, -1)
B. (8,0)
C.(1, -7/8)
D. (-1, 3/2)

Answer 1

D. (-1, 3/2)

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)
• Solving systems of equations using substitution/elimination

Explanation:

Step 1: Define System

4x + 2y = -1

3x + 4y = 3

Step 2: Rewrite System

4x + 2y = -1

1. [Multiplication Property of Equality] Multiply -2 on both sides: -2(4x + 2y) = 2
2. [Distributive Property] Distribute -2 on both sides: -8x - 4y = 2

Step 3: Redefine Systems

-8x - 4y = 2

3x + 4y = 3

Step 4: Solve for x

1. Combine equations: -5x = 5
2. [Division Property of Equality] Divide -5 on both sides: x = -1

Step 5: Solve for y

1. Substitute in x [Original Equation]: 3(-1) + 4y = 3
2. Multiply: -3 + 4y = 3
3. [Addition Property of Equality] Add 3 on both sides: 4y = 6
4. [Division Property of Equality] Divide 4 on both sides: y = 3/2