Which of the following linear equation has a solution x = 7, y = -2?

To get the correct linear equation we will substitute the values of x and y in each given option.

Equation: $2x-5y=4$

$\Rightarrow 2\left(7\right)-5(-2)=4$

$\Rightarrow 14+10=4$

$\Rightarrow 24\ne 4$

So, x = 7, y = -2 is not the solution to this equation.

Equation: $\begin{array}{rcl}2x-3y& =& 5\end{array}$

$\begin{array}{rcl} & \Rightarrow & 2\left(7\right)-3(-2)=5\end{array}$

$\Rightarrow 14+6=5$

$\Rightarrow 20\ne 5$

So, x = 7, y = -2 is not the solution to this equation.

Equation: $2x+5y=4$

$\Rightarrow 2\left(7\right)+5(-2)=4$

$\Rightarrow 14-10=4$

$\Rightarrow 4=4$

Therefore, x = 7, y = -2 is the solution to this equation.

Equation: $2x+y=7$

$\Rightarrow 2(-2)+7=7$

$\Rightarrow -4+7=7$

$\Rightarrow 3\ne 7$

So, x = 7, y = -2 is not the solution to this equation.

Therefore, $2x+5y=4$ is the correct response.