Question

Draw the graph of the following equations and find their point of intersection.

x + y = 4 and 3x – y = 8

Answer 1

1. Identify points for graphing

To draw the graph, we find at least two points (typically intercepts) for each line:

For x + y = 4:

If x = 0, y = 4.

Point: (0, 4).

If y = 0, x = 4.

Point: (4, 0).

For 3x – y = 8:

If x = 0, y = –8.

Point: (0, –8)

If y = 0, 3x = 8

⇒ `x = 8/3 ≈ 2.67`. 

Point: (2.67, 0).

If x = 2, 3(2) – y = 8

⇒ y = –2.

Point: (2, –2).

2. Solve algebraically for the intersection

To find the exact point of intersection, solve the system of equations:

1. x + y = 4
2. 3x – y = 8

Add the two equations together to eliminate y:

(x + y) + (3x – y) = 4 + 8

4x = 12

x = 3

Substitute x = 3 back into the first equation:

3 + y = 4

y = 1

The point of intersection of the lines x + y = 4 and 3x – y = 8 is (3, 1).