Final answer:
The best estimate for the solution of the given system of equations is not listed among the options. After algebraically solving the system, the estimated solution is approximately (6.21, -2.958).
Step-by-step explanation:
The question is asking for the best estimate for the solution to the system of linear equations:
- y = 4x - 19.4
- y = 0.2x - 4.2
To find the solution of the system, we need to determine the point where the two lines intersect. This is the point (x, y) that satisfies both equations simultaneously. To estimate the solution, you can graph these equations and look for the intersection point or solve the system algebraically by setting the two equations equal to each other since they both equal y:
4x - 19.4 = 0.2x - 4.2
Now, we solve for x:
4x - 0.2x = 19.4 + 4.2
3.8x = 23.6
x = 23.6 / 3.8
x = 6.21
Next, we substitute x back into either of the original equations to solve for y. Using the second equation:
y = 0.2(6.21) - 4.2
y = 1.242 - 4.2
y ≈ -2.958
The estimated solution is closest to the ordered pair (6.21, -2.958), which is not listed among the options provided. Therefore, none of the given options are a good estimate for the solution of the system of equations.