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.