Question

5x+7 y=-19 y=-3x-21
find x and y please show your work.

Answer 1

(-8, 3)

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

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

Explanation:

Step 1: Define

5x + 7y = -19

y = -3x - 21

Step 2: Solve for x

Substitution

1. Substitute in y: 5x + 7(-3x - 21) = -19
2. [Distributive Property] Distribute 7: 5x - 21x - 147 = -19
3. Combine like terms: -16x - 147 = -19
4. [Addition Property of Equality] Add 147 on both sides: -16x = 128
5. [Division Property of Equality] Divide -16 on both sides: x = -8

Step 3: Solve for y

1. Define original equation: y = -3x - 21
2. Substitute in x: y = -3(-8) - 21
3. Multiply: y = 24 - 21
4. Subtract: y = 3