$f(x)=2.5 x-18$ and $g(x)=-1.5 x+6$ where $y=f(x)$ and $y=g(x)$. The functions $f$ and $g$ form a system. Find the solution(s) to this system.
One or more solution(s): $(x, y)=$
Preview
No solution
Infinite number of solutions
Answer
Final Answer: The solution to the system of equations is \(\boxed{(6, -3)}\)
Step 1 ：The solution to the system of equations is the point where the two lines intersect. To find this point, we need to set the two equations equal to each other and solve for x. Then, we can substitute this x-value into either of the original equations to find the corresponding y-value.
Step 2 ：Set the two equations equal to each other: \(2.5x - 18 = -1.5x + 6\)
Step 3 ：Solve for x: \(x = 6\)
Step 4 ：Substitute x=6 into either of the original equations to find the corresponding y-value: \(y = 2.5*6 - 18 = -3\)
Step 5 ：Final Answer: The solution to the system of equations is \(\boxed{(6, -3)}\)
