2x+3y=12 4x-3y=5 This is for y=mx+b

1. Add the two equations to eliminate \( y \):

2x + 3y = 12

4x - 3y = 5

(2x + 3y) + (4x - 3y) = 12 + 5

6x = 17

2. Solve for \( x \):

x = \frac{17}{6}

3. Substitute \( x = \frac{17}{6} \) into the first equation to find \( y \):

2\left(\frac{17}{6}\right) + 3y = 12

\frac{34}{6} + 3y = 12

3y = 12 - \frac{34}{6}

3y = \frac{72}{6} - \frac{34}{6}

3y = \frac{38}{6}

y = \frac{38}{18}

y = \frac{19}{9}

4. The equation for \( y = mx + b \) therefore becomes:

y = \frac{17}{6}x - \frac{19}{6}

5. Answer:

y = \frac{17}{6}x - \frac{19}{6}