Do the equations x = 4y + 1 and x = 4y - 1 have the same solution?
How might you explain your answer to someone who has not learned algebra?
To determine if the equations x = 4y + 1 and x = 4y - 1 have the same solution, we can compare the two equations and look for any similarities or differences.
First, let's focus on the expression on the right side of the equal sign. In both equations, we have 4y, which means that the value of y is common in both equations. However, the expressions "+ 1" and "- 1" on the right side make a difference.
Let's consider a simple example to understand this better. Let's say we have the equation x = 4y + 1. To find a possible solution, we can substitute a value for y and solve for x. For instance, if we choose y = 2, we substitute it in the equation:
x = 4(2) + 1
Simplifying, we get:
x = 8 + 1
x = 9
So, with y = 2, the solution to the first equation is x = 9.
Now, let's try the same process with the second equation, x = 4y - 1:
x = 4(2) - 1
Simplifying:
x = 8 - 1
x = 7
So, with y = 2, the solution to the second equation is x = 7.
As we can see from our example, when we substitute the same value of y (2 in this case), we get different solutions for x. Therefore, the two equations, x = 4y + 1 and x = 4y - 1, do not have the same solutions.
To explain this to someone who has not learned algebra, you can use the example above. You may say that both equations have the same value for y, but when we substitute the value of y and solve for x, we get different answers. This means that the equations do not have the same solution.