Question

Decide whether the given ordered pair is a solution of the system2x-y=23x+4y=26 ;(2,2)

Answer 1

The given system of linear equations are:

`\begin{gathered} 2x-y=2 \\ 3x+4y=26 \end{gathered}`

Solving this simultaneously, by the method of elimination, we have:

`\begin{gathered} 2x-y=2\text{ -----eqn i)} \\ 3x+4y=26\text{ ----eqn }ii) \\ We\text{ will eliminate y first by multiplying eqn i) through by 4} \end{gathered}`

Thus, we have:

`\begin{gathered} 8x-4y=8 \\ 3x+4y=26 \\ ----------- \\ 8x+3x=8+26 \\ 11x=34 \\ x=(34)/(11) \end{gathered}`

To find y, substitute the value of x into any of the two(2) equations; thus we have:

`\begin{gathered} \text{From eqn i)} \\ 2x-y=2 \\ 2x-2=y \\ y=2x-2 \\ y=2((34)/(11))-2_{} \\ y=(68)/(11)-(2)/(1) \\ y=(68-22)/(11) \\ y=(46)/(11) \end{gathered}`

Hence, the given ordered pair (2,2) is not a solution to the system