Question 152193
Any problem which has two variables can only be solved if there are at least two equations.
<br>Two numbers whose sum is 23:
x + y = 23
<br>The difference of whose squares is 207: (Let's make x represent the larger of the two):
x<sup>2</sup> - y<sup>2</sup> = 207
<br>Let's solve the first equation for x:
x + y = 23
x = 23 - y
<br>Now we can plug it into the second equation:
x<sup>2</sup> - y<sup>2</sup> = 207
(23-y)<sup>2</sup> - y<sup>2</sup> = 207
23<sup>2</sup> - 46y + y<sup>2</sup> - y<sup>2</sup> = 207
529 - 46y = 207
529 - 207 - 46y = 207 - 207
322 - 46 y = 0
322 = 46y
322/46 = 46y/46
y = 7
<br>Plugging into the first equation:
x = 23 - y
x = 16
<br>Therefore, y = 7 and x = 16