Question

Decide whether the ordered pair is a solution of the system of linear equations. $$ \begin{array}{ll} 3 x-2 y=11 & (5,2) \\ -x+6 y=7 \end{array} $$

Short answer

After performing all the steps, it is concluded that (5,2) is not a solution to the system of equations because the right side of both equations is not equal to the left side after the substitution.

Step-by-step solution

Substitute in Equation 1

Substitute \(x = 5\) and \(y = 2\) into the first equation \(3x – 2y = 11\). The left-hand side therefore becomes \(3(5) - 2(2) = 11.\)

Substitute in Equation 2

Substitute \(x = 5\) and \(y = 2\) into the second equation \(-x + 6y = 7\). The left-hand side therefore becomes \(-5 + 6(2) = 7.\)

Check Equality for Both Equations

If after substituting the values, both equations are found true then the ordered pair (5,2) is a solution to the system of equations, otherwise not.