Question

What are the coordinates of one of the vertices of a rectangle when two sides are given by the lines x - 3y = -8 and 3x + y = 6?

Answer 1

(1, 3)

Explanation:

x - 3y = -8

3x + y = 6

Isolate a variable in one of the equations:

y = 6 - 3x

Substitute the value of y into the other equation:

x - 3(6 - 3x) = -8

Use distributive property:

x - 18 + 9x = -8

Combine like terms:

10x - 18 = -8

Isolate the variable:

10x = 10

x = 1

Substitute the value of x into any equation:

3(1) + y = 6

3 + y = 6

Isolate the variable:

y = 3