Final answer:
To solve the system of equations, multiply the first equation by 6 and the second by 15 to clear the fractions. Then, subtract equation 2 from equation 1 to solve for y. Finally, substitute the value of y back into equation 1 to solve for x.
Step-by-step explanation:
To solve the given system of equations:
1. Multiply the first equation by 6 and the second equation by 15 to clear the fractions:
- 3x + 2y = 12 (equation 1)
- 3x - 10y = 120 (equation 2)
2. Subtract equation 2 from equation 1:
- (3x + 2y) - (3x - 10y) = 12 - 120
- 12y = -108
- y = -9
3. Substitute the value of y back into equation 1 to solve for x:
- 3x + 2(-9) = 12
- 3x - 18 = 12
- 3x = 30
- x = 10
Therefore, the solution to the system of equations is x = 10 and y = -9. The solution is unique.