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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

Solve the following systems of equations to find the point of intersection. a) y = 3x-example-1
User Rauld
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1 Answer

29 votes
29 votes

Given:

The system of equations are:

(a)
y=3x+5


y=-2x+30

(b)
x+y=-3


2y=-2x+8

To find:

The intersection points of the given system of equations.

Solution:

(a)

We have,


y=3x+5 ...(i)


y=-2x+30 ...(ii)

From (i) and (ii), we get


3x+5=-2x+30


3x+2x=30-5


5x=25


x=5

Putting x=5 in (i), we get


y=3(5)+5


y=15+5


y=20

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

(b)

The given system of equations is:


x+y=-3


2y=-2x+8

Write these equation in slope intercept form
(y=mx+b), where m is slope and b is y-intercept.


y=-x-3 ...(iii)


y=-x+4 ...(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.

User Ruben Hensen
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2.7k points