Answer:
A system of equivalent equations is:
x + y = -3
2x - 8y = 2
Explanation:
Given
2x + 2y = -6
x - 4y = 2
Required
Write a system of equivalent equations
A system of equivalent equations implies that:
When the new set of equation is solved, the solution is equivalent to the original equation.
To do this, we have to carry out the same operation on both sides of the given equation.
Take for instance
2x + 2y = -6
Multiply both sides by ½
½(2x + 2y) = -6 * ½
x + y = -3
x + y = -3 is equivalent to 2x + 2y = -6
Multiply both sides of x - 4y = 2 by 2
2(x - 4y) = 2 * 2
2x - 8y = 4
2x - 8y = 4 is equivalent to x - 4y = 2
Hence, a system of equivalent equations is:
x + y = -3
2x - 8y = 2
Note that there are more equivalent equations.
The results you get depend on the operation performed on the given equation.