Q4. Solve the following system of equations by graphing an find the intersection point. 3x+6y=-9 and 4x-6y+16

Check the second equation:  4x-6y+16; should it be 4x - 6y = 16?

If it is:   3x + 6y = -9                                                      4x - 6y  =  16

                 6y  =  -3x - 9                                                      -6y  =  -4x + 16

                    y  =  (-3/6)x - 9/6                                                   y  =  (-4/-6)x + 16/-6

                slope = -1/2                                                       slope = 2/3

        y-intercept =  -3/2                                                   y-intercept = -8/3

Start at point (0,-3/2) on the y-axis                               Start at point (0,-8/3) on the y-axis   

go over 2 and down 3 (place a dot)                                 go over 3 and up 2 (place a dot)

repeat; draw a line.                                                      repeat; draw a line.

If the lines are parallel (slopes are equal and y-intercepts are not equal), they have no solutions.

If the lines are coincident (one in exactly the same place as the other) (slopes are equal and y-interceps are also equal), they have an infinite number of solutions, all the points that they have in common.

If the lines intersect (slopes are not equal), they have one solution, the point where they intersect.

The number of solutions is the number of points in which the two lines cross.

Are you asking Q4. Solve the following system by graphing and finding the intersection point. 3x+6y=-9 and 4x-6y+16?

Yes @ Pyramid