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In a rectangular coordinate system, the line 3y=x intersects the line 2x + 5y = 11 at point A. What is the sum of the coordinates of point A?

A triangular region is bounded by the two coordinate axes and the line given by the equation 2x+y=6. What is the area of the region, in square units?

Guest Apr 10, 2019

edited by Guest Apr 10, 2019

CPhill · Answer 1 · 2019-04-10T12:44:35

x = 3y

2x + 5y = 11 sub the first equation into the second for x

2(3y) + 5y = 11

6y + 5y = 11

11y = 11

y = 1

An d x = 3(1) = 3

So A = (3, 1) .....sum of coordinates = 4

CPhill · Answer 2 · 2019-04-10T12:48:05

Second one....the idea here is to find the x and y intercepts of the line

x intercept....let y = 0

2x + 0 = 6

2x = 6

x = 3

y intercept......let x = 0

2(0) + y = 6

y = 6

Triangle area = (x int) (y int) /2 = (3) (6) / 2 = 9 units^2