Final answer:
To solve the system of equations 6x-3y = 18 and -3x-9y=-93, we can use the method of substitution or elimination. By substituting the value of x into the second equation and solving for y, we find y = 8. Substituting this value back into the first equation gives us x = 7.
Step-by-step explanation:
To solve the system of equations 6x-3y = 18 and -3x-9y=-93, we can use the method of substitution or elimination. Let's use the method of substitution:
- From the first equation, solve for x in terms of y: 6x = 3y + 18 => x = (3y + 18) / 6 = y/2 + 3
- Substitute the value of x into the second equation:
- -3(y/2 + 3) - 9y = -93
- Simplify and solve for y:
- -3y/2 - 9 - 9y = -93
- -3y - 18 - 18y = -186
- -21y = -168
- y = -168 / -21 = 8
- Substitute the value of y back into the first equation to find x:
- 6x - 3(8) = 18
- 6x - 24 = 18
- 6x = 42
- x = 42 / 6 = 7
Therefore, the solution to the system of equations is x = 7 and y = 8.