Question

What is the solution of the system? y= 10x - 3 y= 7x + 2

Answer 1

(5/3, 41/3)

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
• Subtraction Property of Equality

Algebra I

• Terms/Coefficients
• Coordinates (x, y)
• Solving systems of equations using substitution/elimination
• Solving systems of equations by graphing

Explanation:

Step 1: Define Systems

y = 10x - 3

y = 7x + 2

Step 2: Solve for x

Substitution

1. Substitute in y: 10x - 3 = 7x + 2
2. [Subtraction Property of Equality] Subtract 7x on both sides: 3x - 3 = 2
3. [Addition Property of Equality] Add 3 on both sides: 3x = 5
4. [Division Property of Equality] Divide 3 on both sides: x = 5/3

Step 3: Solve for y

1. Define original equation: y = 7x + 2
2. Substitute in x: y = 7(5/3) + 2
3. Multiply: y = 35/3 + 2
4. 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.