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:

$\begin{gathered} 8x-4y=8 \\ 3x+4y=26 \\ ----------- \\ 8x+3x=8+26 \\ 11x=34 \\ x=\frac{34}{11} \end{gathered}$

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

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

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