Question

Solve the system of equations using the elimination method.
3x + 4y = -2
2x + 3y = -1

Answer 1

(-2, 1)

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

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

Explanation:

Step 1: Define Systems

3x + 4y = -2

2x + 3y = -1

Step 2: Rewrite Systems

Find LCM of both equations.

1. [1st Equation] Multiply everything by 2: 6x + 8y = -4
2. [2nd Equation] Multiply everything by -3: -6x - 9y = 3

Step 3: Redefine Systems

6x + 8y = -4

-6x - 9y = 3

Step 4: Solve for y

Elimination

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

Step 5: Solve for x

1. Define original equation: 3x + 4y = -2
2. Substitute in y: 3x + 4(1) = -2
3. Multiply: 3x + 4 = -2
4. [Subtraction Property of Equality] Subtract 4 on both sides: 3x = -6
5. [Division Property of Equality] Divide 3 on both sides: x = -2