Question

the graphs of 2x+3Y=5 and 3x+y=18 contain two sides of a triangle. a vertex of the triangle is at the intersection of the graphs. what are the coordinates of the intersection?

Answer 1

Answer:

(7, - 3 )

Step-by-step explanation:

Solve the 2 equations simultaneously to find intersection.

Given the equations of the sides

2x + 3y = 5 → (1)

3x + y = 18 → (2)

Multiplying (2) by - 3 and adding to (1) will eliminate the y- term

- 9x - 3y = - 54 → (3)

Add (1) and (3) term by term

(2x - 9x) + (3y - 3y) = (5 - 54) and simplifying gives

- 7x = - 49 ( divide both sides by - 7 )

x = 7

Substitute x = 7 into (1) or (2) for corresponding value of y

Substituting in (2)

21 + y = 18 ( subtract 21 from both sides )

y = - 3

Point of intersection = (7, - 3 )