Question

An unknown number y is 15 more than an unknown number x. The number y is also x less than 8. The equations to find x and y are shown below.

y = x + 15
y = −x + 8

Which of the following statements is a correct step to find x and y?

and could somebody please give me a step by step explanation

Answer 1

x = −3.5

y = 11.5

Explanation:

y = x + 15

y = −x + 8

[We know that y is 15 units more than x, and that −x is 8 units less than y. That can be combined into −x + 8 = x + 15 for the first variable (x), and for the second variable (y), y − 15 = −y + 8]

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In order to solve this, solve for the first variable in one of the equations, then substitute the result into the other equation.

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x = −
`(7)/(2)` = −3.5

y =
`(23)/(2)` = 11.5

Answer 2

Since both equations equal y, you can combine them to x+15=-x+8
Next you need to move both variables to the same side so you can subtract x from both sides so it would be 15=-2x+8
Now you want to get the variable alone so you’d subtract the 8 from each side of the equation and you’d be left with 7=-2X
Lastly you one just one x so divide each side by -2 and you’d have 7/-2=x
x= -7/2 or -3.5

Let me know if you want further explanation of how I got x.