Question

6. Solve the following pairs of simultaneous equations.
3x + y = 2
4x + 3y = 3​

Answer 1

x = 3/5, y = 1/5

Explanation:

Starting with:

3x + y = 2

4x + 3y = 3

Multiplying the first equation by -3:

-9x - 3y = -6

4x + 3y = 3

Adding the equations:

-5x = -3

Simplifying:

x = 3/5

Substituting x = 3/5 into the first equation:

9/5 + y = 2

Subtracting:

y = 1/5

Answer 2

(3/5, 1/5)

General Formulas and Concepts:

Pre-Algebra

• Order of Operations: BPEMDAS
• Equality Properties

Algebra I

• Solving systems of equations using substitution/elimination
• Solving systems of equations using graphing

Explanation:

Step 1: Define systems

3x + y = 2

4x + 3y = 3

Step 2: Rewrite systems

y = 2 - 3x

4x + 3y = 3

Step 3: Solve for x

1. Substitute in y: 4x + 3(2 - 3x) = 3
2. Distribute 3: 4x + 6 - 9x = 3
3. Combine like terms: -5x + 6 = 3
4. Isolate x term: -5x = -3
5. Isolate x: x = 3/5

Step 4: Solve for y

1. Define original equation: 3x + y = 2
2. Substitute in x: 3(3/5) + y = 2
3. Multiply: 9/5 + y = 2
4. Isolate y: y = 1/5

Step 5: Check

Graph the systems of equations.