Determine the coordinates of the point of interse3ction of the line defined by the parametric equations and the plane defined by the scalar equation.

Verify that the plane and line are parallel, and then determine if they are distinct or coincident.

\displaystyle \begin{array}{llllllll} &3x + 6y + z -5 = 0 \\ &(x,y, z) = (1, 2, -8) +t(2, -1, -1) \end{array}

Solve each linear system in two-space.

\displaystyle \begin{array}{llllllll} &[x, y] = [-12, -7] + s[8, -5]\\ &[x, y] = [2, -1] + t[3, -2] \end{array}

Verify that the plane and line are parallel, and then determine if they are distinct or coincident.

\displaystyle \begin{array}{llllllll} &x + 2y - 5z + 4 = 0 \\ &(x,y, z) = (10, 3, 4) +t(1, 2, 1) \end{array}

Determine if the plane and line intersect. If so, state the solution.

\displaystyle \begin{array}{llllllll} &3x - y + 4z - 8= 0 &(x,y, z) = (3, 0 , 5) +t(7, -11, -8) \end{array}

Determine if the plane and line intersect. If so, state the solution.

\displaystyle \begin{array}{llllllll} &-2x + 6y + 4z - 4= 0\\ &(x,y, z) = (5, -1, 4) +t(1, -2, 3) \end{array}

Determine the number of solutions for each system without solving.