To determine which of the given systems is equivalent to the system described by the equation 23x + y = 2, x + 12y = 3, we need to analyze both equations.
1. Start with the first equation: 23x + y = 2.
If we solve for y, we get:
y = 2 – 23x
2. Now, let’s look at the second equation: x + 12y = 3.
Rearranging this gives us:
12y = 3 – x
and further simplifying gives:
y = (3 – x) / 12
To find an equivalent system, we can express both equations in a standard format or check if a scaling or substitution can be applied:
Multiply the second equation by 12:
12x + 12(12y) = 12(3)
Which simplifies to:
12x + 144y = 36
3. Now, we can compare the two equations after these transformations. By checking the coefficients or performing elimination methods allows us to seek other systems that yield the same set of solutions.
Based on the transformation and careful evaluation, we find the system that satisfies both equations is an equivalent form. The exact equivalent may only be clear through option checking from a given set of alternatives.
In summary, to determine equivalent systems, rearrangement and manipulation or checking against proposed options will lead you to the answer you need. Always look for ways to express the equations to facilitate comparison.