Solve the following systems of equations to find the point of intersection. a) y = 3x + 5
y = -2x + 30
b) x+y=-3
2y = -2x+8

Given:

The system of equations are:

(a)

(b)

To find:

The intersection points of the given system of equations.

Solution:

(a)

We have,

          ...(i)

         ...(ii)

From (i) and (ii), we get

Putting x=5 in (i), we get

Therefore, the point of intersection is (5,20).

(b)

The given system of equations is:

Write these equation in slope intercept form , where m is slope and b is y-intercept.

         ...(iii)

        ...(iv)

From the equation (iii) and (iv), it is clear that the slopes of both equations are same, i.e., -1 but the y-intercepts are different, -3 and 4 respectively.

It means the lines are parallel and parallel lines never intersect each other.

Therefore, the point of intersect does not exist because the lines are parallel.

if you was gonna solve for a, a is a   < -12

one set of data has more variation than the other. hope this !