Final answer:
The equivalent system of equations is x = -4/17, y = -10/17.
Step-by-step explanation:
To determine the equivalent system for the given system of equations, we need to manipulate the equations in a way that eliminates one of the variables.
Let's start by multiplying the first equation by 10 and the second equation by 4 to ensure that the coefficients of x are equal:
10(4x - 5y) = 10(2)
4(10x - 21y) = 4(10)
Now, we can simplify these equations:
40x - 50y = 20
40x - 84y = 40
Subtracting the second equation from the first equation:
(40x - 50y) - (40x - 84y) = 20 - 40
34y = -20
Dividing both sides by 34:
y = -20/34
Simplifying the fraction:
y = -10/17
Now, we substitute this value of y back into one of the original equations to solve for x. Let's use the first equation:
4x - 5(-10/17) = 2
4x + 50/17 = 2
Subtracting 50/17 from both sides:
4x = 2 - 50/17
4x = 34/17 - 50/17
4x = -16/17
Dividing both sides by 4:
x = -16/68
Simplifying the fraction:
x = -4/17
Therefore, the equivalent system of equations is:
x = -4/17, y = -10/17