Question

question 23 of 25
use the elimination method to solve the system of equations. choose the correct ordered pair.
$x + y = 9$
$x - y = 7$
a. (7, 0)
b. (8, 1)
c. (16, -7)
d. (12, -3)

Explanation:

Step1: Eliminate y by adding equations

Add the two equations \( x + y = 9 \) and \( x - y = 7 \) together.
\( (x + y) + (x - y) = 9 + 7 \)
Simplify the left side: \( x + y + x - y = 2x \)
Simplify the right side: \( 16 \)
So, \( 2x = 16 \)

Step2: Solve for x

Divide both sides of \( 2x = 16 \) by 2.
\( x = \frac{16}{2} = 8 \)

Step3: Substitute x into one equation to find y

Substitute \( x = 8 \) into \( x + y = 9 \).
\( 8 + y = 9 \)
Subtract 8 from both sides: \( y = 9 - 8 = 1 \)

Answer:

B. (8, 1)