Question

Solve graphically:

x + y = 4, 3x + y = 6

Answer 1

To solve the system of equations graphically:

x + y = 4

3x + y = 6

We can plot each line on a coordinate plane by finding two or more points for each.

Step 1: Find points for the first line (x + y = 4).

We can rewrite this as y = 4 – x.

If x = 0, then y = 4 – 0 = 4.

Point: (0, 4)

If x = 4, then y = 4 – 4 = 0.

Point: (4, 0)

If x = 1, then y = 4 – 1 = 3.

Point: (1, 3)

Step 2: Find points for the second line (3x + y = 6).

We can rewrite this as y = 6 – 3x.

If x = 0, then y = 6 – 3(0) = 6.

Point: (0, 6)

If x = 2, then y = 6 – 3(2) = 0.

Point: (2, 0)

If x = 1, then y = 6 – (3)1 = 3.

Point: (1, 3)

Step 3: Plot the lines and find the intersection

Plotting these points and drawing lines through them:

The two lines intersect at the point where both equations are satisfied. From the graph and the calculated points, we see they cross at (1, 3).