Question

PLEASE HELP ME WITH THIS QUESTION

what is the equation of a line that joins the point of intersection of 5x-2y+3=0 and 4x-3y+1=0 to the point of intersection of x=y and x=3y+4?​

Answer 1

Answer: y = x

Explanation:

First, find the point where 5x - 2y + 3 and 4x - 3y + 1 intersect using the Elimination Method.

5x - 2y + 3 = 0 → 3(5x - 2y + 3 = 0) → 15x - 6y + 9 = 0

4x - 3y + 1 = 0 → -2(4x - 3y + 1 = 0) → -8x + 6y - 2 = 0

7x + 7 = 0

7x = -7

x = -1

5x - 2y + 3 = 0

5(-1) - 2y + 3 = 0

-5 - 2y + 3 = 0

-2y - 2 = 0

-2y = 2

y = -1

(-1, -1)

Next, find the point where x = y and x = 3y + 4 intersect using the Substitution Method.

x = y

x = 3y + 4 → y = 3y + 4

-2y = 4

y = -2

x = y

x = -2

(-2, -2)

Now, find the line that passes through (-1, -1) and (-2, -2) using the Point-Slope formula. (x₁, y₁) = (-1, -1) and m = 1

y - y₁ = m(x - x₁)

y + 1 = 1(x + 1)

y = x