Answer:
(x,y) = (-2,4)
Step-by-step explanation:
We have two equations:
[tex](1).\:2x+5y=16\\(2).-5x-2y=2[/tex]
Now let us us multiply equation (1) by 5, and equation (2) by 2:
[tex](1).\:5(2x+5y=16)\rightarrow\:10x+25y=80\\\\(2).2(-5x-2y=2)\rightarrow\:-10x-4y=4[/tex]
and add the two equations to get:
[tex]21y=84[/tex]
[tex]\boxed{y=4}[/tex]
Now we put this value of [tex]y[/tex] into equation(1) and solve for [tex]x[/tex] :
[tex]2x+5(4)=16[/tex]
[tex]2x=-4[/tex]
[tex]\boxed{x=-2}[/tex]
Thus the solution to our system of equations is
[tex]\boxed{(x,y)=(-2,4)}[/tex]
