Given
The equations are given
[tex]\begin{gathered} -5x+y=-5\ldots\ldots\ldots\ldots1 \\ -4x+2y=2\ldots\ldots\ldots\ldots\ldots\text{.}.2 \end{gathered}[/tex]
Explanation
To determine the coordinates of x and y by elimination method.
Divide equation 2 by 2.
[tex]\begin{gathered} -\frac{4x}{2}+\frac{2y}{2}=\frac{2}{2} \\ -2x+y=1\ldots\ldots\ldots\ldots..3 \end{gathered}[/tex]
Now subtract equation 1 by 3,
[tex]\begin{gathered} (-5x+y+5)-(-2x+y-1)=0 \\ -5x+y+5+2x-y+1=0 \\ -3x+6=0 \\ x=2 \end{gathered}[/tex]
Substitute the value of x in the equation 1.
[tex]\begin{gathered} -5\times2+y=-5 \\ -10+y=-5 \\ y=5 \end{gathered}[/tex]
Answer
The solution of the system of equations is
[tex](2,5)[/tex]
The correct option is A.
