Question Type 2: Finding the intersection points between two different lines Exercises

Find the intersection of the lines $y = -3x + 7$ and $y = 2x - 5$.

Solve for the intersection of $y = 0.5x - 2$ and $x - y = 6$.

Calculate the intersection of the lines $x + y = 4$ and $2x + 2y = 10$.

Find the point where the lines $\frac{x}{2} + \frac{y}{3} = 1$ and $y = -2x + 4$ intersect.

Determine the intersection point of the line $4x - 2y = 8$ with the line $y = x + 1$.

Determine the intersection of the line $y = 3x - 4$ and the perpendicular line through $(3,4)$.

Two roads are modeled by $y = 0.8x + 5$ and $y = -1.2x + 20$. At what point do they meet?

A supplier’s cost is $C_1(x) = 50x + 200$ and a competitor’s is $C_2(x) = 30x + 500$. At what production level $x$ are the costs equal?

Find the intersection point of the line passing through $(1, 2)$ and $(3, 6)$ and the line passing through $(-2, 8)$ and $(4, -2)$.

Calculate the intersection point of the lines $y = 5x + 4$ and $y = 2x - 3$.

Find the intersection point of $3x + 4y = 12$ and $5x - 2y = 7$.