Question

What is the y value of the solution to the system of equations given? y=5x-3 3x-2y=27

Answer 1

y = -18

General Formulas and Concepts:

Pre-Algebra

• Order of Operations: BPEMDAS
• Equality Properties

Algebra I

• Solving systems of equations using substitution/elimination

Explanation:

Step 1: Define systems

y = 5x - 3

3x - 2y = 27

Step 2: Rewrite systems

1. Define: 3x - 2y = 27
2. Add 2y on both sides: 3x = 2y + 27
3. Divide 3 on both sides: x = 2/3y + 9

Step 3: Redefine

y = 5x - 3

x = 2/3y + 9

Step 4: Solve for y

1. Substitute in x: y = 5(2/3y + 9) - 3
2. Distribute 5: y = 10/3y + 45 - 3
3. Combine like terms: y = 10/3y + 42
4. Subtract 10/3y on both sides: -7/3y = 42
5. Divide -7/3 on both sides: y = -18