(also pictured)

two sides of a rectangle have the equations y=2x and 2y+x=5. find, algebraically, the coordinates of the vertex of the rectangle formed by these sides.

Hello,

The slope of the 1st side is 2 (y=2x)
The slope of the 2 nd side is -1/2 (y=-x/2+5/2)
The two sides are perpendicular so we can find the  vertex.

y=2x (1)
2y+x=5
If we substitue y by is value in (1)
2(2x)+x=5==>5x=5
==>x=1 and y=2*1=2
Vertex is (1,2)
In order to find the rectangle we must know an other vertex.