Question

What is the solution to the pair of simultaneous equations? 2x+y=5. 3x-2y=4​

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

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

2x + y = 5

3x - 2y = 4

Step 2: Rewrite Systems

Manipulate 1st equation

1. [Subtraction Property of Equality] Subtract 2x on both sides: y = 5 - 2x

Step 3: Solve for x

Substitution

1. Substitute in y [2nd Equation]: 3x - 2(5 - 2x) = 4
2. [Distributive Property] Distribute -2: 3x - 10 + 4x = 4
3. [Addition] Combine like terms: 7x - 10 = 4
4. [Addition Property of Equality] Add 10 on both sides: 7x = 14
5. [Division Property of Equality] Divide 7 on both sides: x = 2

Step 4: Solve for y

1. Substitute in x [Modified 1st Equation]: y = 5 - 2(2)
2. Multiply: y = 5 - 4
3. Subtract: y = 1