Final answer:
To find an equivalent system of equations, multiply the first equation by 5 and the second equation by 2. Then, add the two new equations together. The equivalent system of equations is X = 0 and y = 1.
Step-by-step explanation:
To find an equivalent system of equations, we can manipulate the given equations to create a new set of equations with the same solution. Let's start with the given system:
2X + 4y = 4
-5x + 5y = 5
To eliminate the variable 'x', multiply the first equation by 5 and the second equation by 2:
10X + 20y = 20
-10x + 10y = 10
Now, add the two new equations together:
10X + 20y + (-10x + 10y) = 20 + 10
Simplifying the equation, we get:
30y = 30
Dividing both sides by 30, we find:
y = 1
Now, substitute the value of 'y' into the first equation to solve for 'x':
2X + 4(1) = 4
2X + 4 = 4
Subtracting 4 from both sides gives us:
2X = 0
Dividing both sides by 2, we get:
X = 0
Therefore, the equivalent system of equations is:
X = 0
y = 1