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?
Accepted Solution
A:
Answer: y = xStep-by-step 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 = 04x - 3y + 1 = 0 → -2(4x - 3y + 1 = 0) → -8x + 6y - 2 = 0 7x + 7 = 0 7x = -7 x = -15x - 2y + 3 = 05(-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 = yx = 3y + 4 → y = 3y + 4 -2y = 4 y = -2x = yx = -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 = 1y - y₁ = m(x - x₁)y + 1 = 1(x + 1) y = x