The estimated solution to the system of equations is x = -7/2 and y = -1/2. Represented as a mixed number, x = -3 1/2. The closest match among the options is C. x = -1 2/5, y = 1 3/5.
To estimate the solution to the system of equations -3x + 3y = 9 and 2x - 7y = -14, we can use the elimination method:
Multiply the first equation by 2 to make the coefficients of x in both equations equal:
-6x + 6y = 18
Now, the system becomes:
-6x + 6y = 18
2x - 7y = -14
Adding these equations eliminates x:
-x - y = 4
Now, solving for y:
y = -x - 4
Substitute this expression for y into one of the original equations, let's use the first one:
-3x + 3(-x - 4) = 9
Simplify:
-3x - 3x - 12 = 9
Combine like terms:
-6x - 12 = 9
Add 12 to both sides:
-6x = 21
Divide by -6:
x = -7/2
Now substitute this value of x back into the expression for y:
y = -(-7/2) - 4 = 7/2 - 4 = -1/2
So, the estimated solution is x = -7/2 and y = -1/2.
To represent the solution as a mixed number, x = -7/2 can be expressed as x = -3 1/2.
Therefore, the closest match from the given options is:
C. x = -1 2/5, y = 1 3/5.