Question

solve the same using the Elimination method if there is no solution put no solution if there is infinite put infinite7.5p + k = 922.5p +3k =6

Answer 1

The system of equations is given as,

`\begin{gathered} 7.5p+k=9 \\ 22.5p+3k=6 \end{gathered}`

Let us eliminate the variable 'k' first.

The coefficient can be made equal by multiplying the first equation by 3,

`\begin{gathered} (7.5p+k)\cdot3=9\cdot3 \\ 22.5p+3k=6 \end{gathered}`

Simplify the system of equations,

`\begin{gathered} 22.5p+3k=27 \\ 22.5p+3k=6 \end{gathered}`

Subtract the second equation from the first,

`\begin{gathered} (22.5p+3k)-(22.5p+3k)=27-6 \\ 22.5p+3k-22.5p-3k=21 \\ 0=21 \end{gathered}`

Note that the result obtained does not hold true for any values of 'p' and 'k'.

So the given system of linear equations will have no solution.