Question Type 2: Finding points of intersection of two straight lines Exercises

Solve for the intersection of the lines $\frac{3}{2}x - \frac{1}{3}y = 4$ and $\frac{x}{4} + \frac{y}{2} = 1$.

Find the point of intersection of the lines $4x + y = 8$ and $x - 3y = 1$.

Determine whether the lines $2x - 4y + 2 = 0$ and $x - 2y + 1 = 0$ intersect; if so, find all solutions.

Do the lines $y = 3x + 2$ and $6x - 2y + 1 = 0$ intersect? If so, find the point.

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

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

Solve for the intersection of the lines given by $3x - y = 7$ and $x + 2y = 4$.

Find the intersection of the lines $5x - 2y + 10 = 0$ and $x + y - 3 = 0$.

Determine the intersection point of the lines $y = -x + 1$ and $y = 2x - 5$.

Determine the intersection point of the lines $2x + 3y = 12$ and $4x - y = 6$.

Find the intersection of the lines $2x - 5y + 3 = 0$ and $5x + 2y - 11 = 0$.

A line passes through $(1, 2)$ and $(3, 6)$. Find its intersection with the line $y = -x + 4$.