Question

use the substitution method to solve the system of equations. choose the correct ordered pair.

$x + y = 12$
$-x = -y - 10$

a. $(9, 3)$
b. $(11, 1)$
c. $(10, 2)$
d. $(8, 4)$

Explanation:

Step1: Simplify the second equation

From \(-x = -y - 10\), multiply both sides by \(-1\) to get \(x = y + 10\).

Step2: Substitute \(x\) into the first equation

Substitute \(x = y + 10\) into \(x + y = 12\), we have \((y + 10) + y = 12\).
Simplify the left side: \(2y + 10 = 12\).
Subtract 10 from both sides: \(2y = 12 - 10 = 2\).
Divide both sides by 2: \(y = \frac{2}{2} = 1\).

Step3: Find the value of \(x\)

Substitute \(y = 1\) into \(x = y + 10\), we get \(x = 1 + 10 = 11\).

Answer:

B. (11, 1)