Question

determine whether the ordered pair (5,1) is a solution to the given system of equations.
x + 3y = 8
y = 2x - 9
ordered pair (5,1) does not satisfy equations, so it is not the solution to the system of equations. the ordered pair (5, 1) satisfies both equations, so it is the solution to the system of equations.

Explanation:

Step1: Check first equation

Substitute \(x = 5\), \(y = 1\) into \(x + 3y = 8\).
Left side: \(5 + 3\times1 = 5 + 3 = 8\), right side: \(8\). So it satisfies the first equation.

Step2: Check second equation

Substitute \(x = 5\) into \(y = 2x - 9\).
\(y = 2\times5 - 9 = 10 - 9 = 1\), which matches the given \(y = 1\). So it satisfies the second equation.

Answer:

The ordered pair \((5,1)\) satisfies both equations, so it is the solution to the system of equations.