Question

Solve the system.

3x=y+2

3x+2y=5

The solution is ____


Explain your choice of method.

Answer 1

(1, 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

Algebra I

• Solving systems of equation using substitution/elimination

Explanation:

Step 1: Define Systems

3x = y + 2

3x + 2y = 5

Step 2: Rewrite Systems

3x = y + 2

1. Subtract 2 on both sides: 3x - 2 = y
2. Rewrite: y = 3x - 2

Step 3: Redefine Systems

y = 3x - 2

3x + 2y = 5

Step 4: Solve for x

Substitution

1. Substitute in y: 3x + 2(3x - 2) = 5
2. Distribute 2: 3x + 6x - 4 = 5
3. Combine like terms: 9x - 4 = 5
4. Isolate x term: 9x = 9
5. Isolate x: x = 1

Step 5: Solve for y

1. Define equation: 3x + 2y = 5
2. Substitute in x: 3(1) + 2y = 5
3. Multiply: 3 + 2y = 5
4. Isolate y term: 2y = 2
5. Isolate y: y = 1