Question

The point of intersection of 3x-y=4 and x-y=8 is

Answer 1

The point of intersection of 3x-y=4 and x-y=8 is

Answer 2

The point of intersection is (-2,-10)

Step-by-step explanation:

Given: Equation of lines: 3x - y = 4 and x - y = 8

To Find: The point of intersection (x,y)

Solution:

• Finding the point of intersection between lines 3x-y=4 and x-y=8

For lines a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0, the point of intersection can be determined by the follwing formula:

$(x,y) = \Big( \frac{b_1 c_2 - b_2 c_1}{a_1 b_2 - a_2 b_1} , \frac{a_2 c_1 - a_1 c_2}{a_1 b_2 - a_2 b_1} \Big)$

Considering the given equation of lines, we have a₁ = 3, b₁ = -1, c₁ = -4, a₂ = 1, b₂ = -1, and c₂ = -8, we get:

$(x,y) = \Big( \frac{(-1) (-8) - (-1) (-4)}{(3) (-1) - (1) (-1)} , \frac{(1) (-4) - (3) (-8)}{(3) (-1) - (1) (-1)} \Big)$

$\Rightarrow (x,y) = \Big( \frac{8-4}{-3+1} , \frac{-4+24}{-3+1} \Big)$

$\Rightarrow (x,y) = (-2 , -10)$

Hence, the point of intersection of the equation of lines 3x - y = 4 and x - y = 8  is (-2,-10)