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 right-hand sides of both equations.
The first equation x = 4y + 1 means that whatever value y takes, you multiply it by 4 and then add 1 to get the value of x. So if y is 1, x would be 5 (4 * 1 + 1 = 5). Likewise, if y is 2, x would be 9 (4 * 2 + 1 = 9). This pattern continues for any value of y.
Similarly, the second equation x = 4y - 1 means that whatever value y takes, you multiply it by 4 and then subtract 1 to get the value of x. For example, if y is 1, x would be 3 (4 * 1 - 1 = 3). If y is 2, x would be 7 (4 * 2 - 1 = 7), and so on.
Now, if we examine the two sets of values for x based on different values of y, we can see that in the first equation, x will always be 1 more than the value it takes in the second equation. So, the solutions to the equations will never be the same.
To summarize, the equations x = 4y + 1 and x = 4y - 1 do not have the same solution. In the first equation, x will always be 1 more than the value it takes in the second equation.