Respuesta :
Solution:
Given:
[tex]\begin{gathered} -5x+7y=11 \\ -5x+3y=19 \end{gathered}[/tex]The variable that has the same term is x. This is because the coefficient of x in both equations is -5.
To solve simultaneously by the elimination method, we eliminate the variable that has the same term.
Hence, we eliminate x and solve for y.
To eliminate x, we subtract both equations.
[tex]\begin{gathered} -5x+7y=11\ldots\ldots\ldots\ldots\ldots\ldots\text{.}\mathrm{}(1) \\ -5x+3y=19\ldots\ldots\ldots\ldots\ldots\ldots.(2) \\ \\ \text{Subtracting equation (2) from equation (1),} \\ \text{That is equation (1) - (2);} \\ -5x-(-5x)+7y-3y=11-19 \\ -5x+5x+7y-3y=11-19 \\ 4y=-8 \\ \text{Dividing both sides by 4 to get y,} \\ y=-\frac{8}{4} \\ y=-2 \end{gathered}[/tex]Substituting the value of y in equation (1) to get x,
[tex]\begin{gathered} -5x+7y=11 \\ -5x+7(-2)=11 \\ -5x-14=11 \\ -5x=11+14 \\ -5x=25 \\ \text{Dividing both sides by -5 to get x,} \\ x=\frac{25}{-5} \\ x=-5 \end{gathered}[/tex]Therefore, the solution to the system of equations as an ordered pair is,
[tex](x,y)=(-5,-2)[/tex]