Question

1. use a method of your choice to solve this system of equations. show all of your work and write your solution as an ordered pair.

$x + y = 6$
$7x + 12y = 52$

Explanation:

Step1: Solve for x from first equation

From \( x + y = 6 \), we get \( x = 6 - y \).

Step2: Substitute x into second equation

Substitute \( x = 6 - y \) into \( 7x + 12y = 52 \):
\( 7(6 - y) + 12y = 52 \)
\( 42 - 7y + 12y = 52 \)
\( 42 + 5y = 52 \)

Step3: Solve for y

Subtract 42 from both sides: \( 5y = 52 - 42 = 10 \)
Divide by 5: \( y = \frac{10}{5} = 2 \)

Step4: Solve for x

Substitute \( y = 2 \) into \( x = 6 - y \): \( x = 6 - 2 = 4 \)

Answer:

The ordered pair is \((4, 2)\)