Solve using substitution method 2x+3y=12 4x-3y=15

1. Start with the system of equations:
2x + 3y = 12
4x - 3y = 15

2. Solve the first equation for \( x \):
2x + 3y = 12
2x = 12 - 3y
x = \frac{12 - 3y}{2}

3. Substitute \( x = \frac{12 - 3y}{2} \) into the second equation:
4\left(\frac{12 - 3y}{2}\right) - 3y = 15
2(12 - 3y) - 3y = 15
24 - 6y - 3y = 15
24 - 9y = 15

4. Solve for \( y \):
-9y = 15 - 24
-9y = -9
y = 1

5. Substitute \( y = 1 \) back into the equation for \( x \):
x = \frac{12 - 3(1)}{2}
x = \frac{12 - 3}{2}
x = \frac{9}{2}

6. The solution to the system of equations is:
x = \frac{9}{2}, \, y = 1