Question

The graph 2x + 3y = 5 and 3x + y= 18 contqin two sides of a triangle. A vertex of the triangle is at the intersection of the graphs. What are the coordinates of the vertex

Answer 1

(2x + 3y) - (3x + y) = 5 - 18

2x + 3y - 3x - y = -13

-x + 2y = -13

we rewrite the equation by changing the signs

x- 2y = 13

solve the equation for x as a function of y

x = 13 + 2y

substitute x into one of the equations to find the value of y. For example, we'll use the equation 3x + y = 18.

3(13 + 2y) + y = 18

39 + 6y + y = 18

7y = 18 - 39

7y = -21

y = -3

we calculate x :

x = 13 + 2(-3) = 13 - 6 = 7

the coordinates of the vertex of the triangle are (7, -3)