Enter your answer and show all the steps that you use to solve this problem in the space provided. Solve the system by substitution. {−4.5x−2y=−12.5 3.25x−y=−0.75}
First, we solve the second equation for y:
3.25x - y = -0.75
y = 3.25x + 0.75
Now, we substitute this value for y into the first equation:
-4.5x - 2(3.25x + 0.75) = -12.5
-4.5x - 6.5x - 1.5 = -12.5
-11x - 1.5 = -12.5
-11x = -12 - 1.5
-11x = -13.5
x = -13.5 / -11
x = 1.2273 (rounded to four decimal places)
Next, we substitute this value for x into the second equation to find y:
y = 3.25(1.2273) + 0.75
y = 3.9898 (rounded to four decimal places)
Therefore, the solution to the system of equations is x = 1.2273 and y = 3.9898.