Question

Determine the point on the graph of the equation 3x + 5y = 25 whose x-coordinate is 5/
3
times its ordinate.
Also, find the points where the given line cuts the x-axis and y-axis. ​

Answer 1

Answer:

The locus of points equidistant from the coordinate axes is the pair of lines y=x and y=−x.

Solve simultaneously 3x+5y=15 and y=x to obtain x=y=

8

15

.The point (

8

15

,

8

15

)in quadrant I, therefore satisfies the required condition. Solve simultaneously 3x+5y=15 and y=−x to obtain x=−

2

15

,y=

2

15

. The point (−

2

15

,

2

15

) in quadrant II, therefore satisfies the required conditions.

There are no other solutions to these pairs of equations, and, therefore, no other points satisfying the required condition.