Answer:
(3, 0)
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
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
Step-by-step explanation:
Step 1: Define Systems
3x - y = 9
2x - y = 6
Step 2: Rewrite Systems
2x - y = 6
- Subtract 2x on both sides: -y = 6 - 2x
- Divide -1 on both sides: y = 2x - 6
Step 3: Redefine Systems
3x - y = 9
y = 2x - 6
Step 4: Solve for x
Substitution
- Substitute in y: 3x - (2x - 6) = 9
- Distribute -1: 3x - 2x + 6 = 9
- Combine like terms: x + 6 = 9
- Isolate x: x = 3
Step 5: Solve for y
- Define equation: 2x - y = 6
- Substitute in x: 2(3) - y = 6
- Multiply: 6 - y = 6
- Isolate y term: -y = 0
- 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.
