Question

Solve the following system of equations. -3x + 4y = 64 x + 4y = 32

Answer 1

(-8, 10)

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
• Subtract Property of Equality

Algebra I

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

Explanation:

Step 1: Define Systems

-3x + 4y = 64

x + 4y = 32

Step 2: Rewrite Systems

x + 4y = 32

1. [Subtract Property of Equality] Subtract 4y on both sides: x = 32 - 4y

Step 3: Redefine Systems

-3x + 4y = 64

x = 32 - 4y

Step 4: Solve for y

Substitution

1. Substitute in x: -3(32 - 4y) + 4y = 64
2. Distribute -3: -96 + 12y + 4y = 64
3. Combine like terms: 16y - 96 = 64
4. [Addition Property of Equality] Add 96 on both sides: 16y = 160
5. [Division Property of Equality] Divide 16 on both sides: y = 10

Step 5: Solve for x

1. Define equation: x + 4y = 32
2. Substitute in y: x + 4(10) = 32
3. Multiply: x + 40 = 32
4. [Subtraction Property of Equality] Subtract 40 on both sides: x = -8