Answer: y = x
Step-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 = 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
