Question

solve the system of equations below.
$x - 2y = 3$
$2x - 3y = 9$
a. $(-3, 9)$
b. $(-9, 3)$
c. $(3, 9)$
d. $(9, 3)$

Explanation:

Step1: Solve for x from first equation

From \( x - 2y = 3 \), we get \( x = 3 + 2y \).

Step2: Substitute x into second equation

Substitute \( x = 3 + 2y \) into \( 2x - 3y = 9 \):
\( 2(3 + 2y) - 3y = 9 \)
\( 6 + 4y - 3y = 9 \)
\( 6 + y = 9 \)
\( y = 9 - 6 = 3 \)

Step3: Find x using y=3

Substitute \( y = 3 \) into \( x = 3 + 2y \):
\( x = 3 + 2\times3 = 3 + 6 = 9 \)

Answer:

D. (9, 3)