Question

Determine whether the lines given by the fallowing equations intersect at (-1/4,3/4) show all work. 4x+8y=5, x-3y= -3

Answer 1

(0, 1)

Explanation:

First, we need to make y the subject of the formula from both expressions

For 4x+8y=5

8y = 5- 4x

y = (5-4x)/5

Similarly for x-3y= -3

-3y = -3 - x

3y = x+3

y = (x+3)/3

Since both lines intersects, hence;

(5-4x)/5 = (x+3)/3

Cross multiply

5(x+3) = 3(5-4x)

5x + 15 = 15 - 12x

5x + 12x = 15 - 15

17x = 0

x = 0/17

x = 0

Sustitute x = 0 into any of the equations

Given that y = x+3/3

y = 0+3/3

y = 3/3

y = 1

This shows that the lines intesects at (0, 1)