Question

solve the system of equations. note: this is an example of a problem that will be done on paper. x - 2y = 1 2x + y = 12 (x, y) = ( , )

Explanation:

Step1: Solve for x from first equation

From \( x - 2y = 1 \), we get \( x = 2y + 1 \).

Step2: Substitute x into second equation

Substitute \( x = 2y + 1 \) into \( 2x + y = 12 \):
\( 2(2y + 1) + y = 12 \)
Expand: \( 4y + 2 + y = 12 \)
Combine like terms: \( 5y + 2 = 12 \)
Subtract 2: \( 5y = 10 \)
Divide by 5: \( y = 2 \).

Step3: Find x using y

Substitute \( y = 2 \) into \( x = 2y + 1 \):
\( x = 2(2) + 1 = 5 \).

Answer:

\((5, 2)\)