Question

Determine the solution to the system of equations.
3x - y = 9
2x - y = 6

Answer 1

isolate and solve for y

Explanation:

subtract y from both sides than divide the x values from bothe sides

Answer 2

(3, 0)

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
• Subtract Property of Equality

Algebra I

• Solving systems of equations using substitution/elimination
• Solving systems of equations by graphing
• Terms/Coefficients

Explanation:

Step 1: Define Systems

3x - y = 9

2x - y = 6

Step 2: Rewrite Systems

2x - y = 6

1. Subtract 2x on both sides: -y = 6 - 2x
2. Divide -1 on both sides: y = 2x - 6

Step 3: Redefine Systems

3x - y = 9

y = 2x - 6

Step 4: Solve for x

Substitution

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

Step 5: Solve for y

1. Define equation: 2x - y = 6
2. Substitute in x: 2(3) - y = 6
3. Multiply: 6 - y = 6
4. Isolate y term: -y = 0
5. Isolate y: y = 0

Step 6: Check

Graph the systems to verify the solution set (3, 0) is the solution.

The solution set to the systems would be where the 2 lines intersect.

We see that the intersection point is x-intercept (3, 0).

∴ (3, 0) is the solution set to the systems of equations.