Answer: 7 and 8
<u>Step-by-step explanation:</u>
Let x represent the first number, then x + 1 is the other number.
(x)² + (x + 1)² = 113
x² + x² + 2x + 1 = 113 <em>expanded (x + 1)²</em>
2x² + 2x + 1 = 113 <em>added like terms</em>
2x² + 2x - 112 = 0 <em>subtracted 113 from both sides</em>
x² + x - 56 = 0 <em> divided both sides by 2</em>
(x + 8) (x - 7) = 0 <em>factored polynomial</em>
x + 8 = 0 x - 7 = 0 <em>applied zero product property</em>
x = -8 x = 7 <em> solved for x</em>
↓
not valid since the restriction is that x > 0 <em>(a positive number)</em>
So, x = 7 and x + 1 = (7) + 1 = 8
<h3><u>The value of x is 19.</u></h3><h3><u>The value of y is 4.</u></h3>
x = 3 + 4y
x + y = 23
Because we have a value for x we can plug it directly into the second equation.
3 + 4y + y = 23
Subtract 3 from both sides.
4y + y = 20
Combine like terms.
5y = 20
Divide both sides by 5.
y = 4
Plug this value for x back into the original equation.
x = 3 + 4(4)
x = 3 + 16
x = 19
