Answer:
(5/3, 41/3)
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
- Subtraction Property of Equality
Algebra I
- Terms/Coefficients
- Coordinates (x, y)
- Solving systems of equations using substitution/elimination
- Solving systems of equations by graphing
Step-by-step explanation:
Step 1: Define Systems
y = 10x - 3
y = 7x + 2
Step 2: Solve for x
Substitution
- Substitute in y: 10x - 3 = 7x + 2
- [Subtraction Property of Equality] Subtract 7x on both sides: 3x - 3 = 2
- [Addition Property of Equality] Add 3 on both sides: 3x = 5
- [Division Property of Equality] Divide 3 on both sides: x = 5/3
Step 3: Solve for y
- Define original equation: y = 7x + 2
- Substitute in x: y = 7(5/3) + 2
- Multiply: y = 35/3 + 2
- Add: y = 41/3
Step 4: Check
Verify the solution set to the systems of equations by graphing the systems.
Where the 2 lines intersect is the solution set to the systems of equations.
We see graphically that point (1.666667, 13.66667), equivalent to (5/3, 41/3).
∴ (5/3, 41/3) or x = 5/3 and y = 41/3 is the solution to the systems of equations.
