Question

which of the following (x,y) pairs is the solution for the system of equations x + 2y = 8 and -2x + y = 14?

Explanation:

Step1: Solve the first equation for x

From \( x + 2y = 8 \), we get \( x = 8 - 2y \).

Step2: Substitute x into the second equation

Substitute \( x = 8 - 2y \) into \( -2x + y = 14 \):

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Step3: Find x using y = 6

Substitute \( y = 6 \) into \( x = 8 - 2y \):
\( x = 8 - 2\times6 = 8 - 12 = -4 \)

Answer:

The solution is \((-4, 6)\)