Question

1. the sum of two numbers is 44. one number is 2 more than twice the other. write a system of equations that defines this situation and solve using any method.

Explanation:

Step1: Define variables for numbers

Let the two numbers be $x$ and $y$.

Step2: Set up sum equation

$x + y = 44$

Step3: Set up relationship equation

$x = 2y + 2$

Step4: Substitute $x$ into sum equation

$(2y + 2) + y = 44$

Step5: Simplify and solve for $y$

$3y + 2 = 44$
$3y = 44 - 2 = 42$
$y = \frac{42}{3} = 14$

Step6: Solve for $x$ using $y=14$

$x = 2(14) + 2 = 28 + 2 = 30$

Answer:

System of equations:
$x + y = 44$
$x = 2y + 2$

The two numbers are 30 and 14.