Final answer:
To solve the system of equations -0.9x + 1.4y = 8 and 3.6x - 0.6y = 3, we can use the method of substitution. The solution is (20.67, 19).
Step-by-step explanation:
To solve the system of equations -0.9x + 1.4y = 8 and 3.6x - 0.6y = 3, we can use the method of substitution. First, solve one equation for x or y and substitute it into the other equation.
Let's solve the first equation for x:
-0.9x + 1.4y = 8 ----> -0.9x = 8 - 1.4y ----> x = (8 - 1.4y) / -0.9
Now substitute this value of x into the second equation:
3.6((8 - 1.4y) / -0.9) - 0.6y = 3
Simplify and solve for y:
-12.96 + 1.44y - 0.6y = 3 ----> -12.96 + 0.84y = 3 ----> 0.84y = 15.96 ----> y = 15.96 / 0.84 = 19
Now substitute the value of y back into the first equation to find x:
-0.9x + 1.4(19) = 8 ----> -0.9x + 26.6 = 8 ----> -0.9x = -18.6 ----> x = -18.6 / -0.9 = 20.67
Therefore, the solution to the system of equations is (20.67, 19). None of the given options match this solution.