Question

Solve the linear equations \(3x + y = 14\) and \(y = 2\) graphically.

Hint:

When solving graphically, choose \(x\) values that result in integer \(y\) values to make plotting easier and more accurate on grid paper.

Answer 1

Step 1: Convert First Equation into Slope Form
Given equation:
3x + y = 14

Rewrite as:
y = 14 − 3x

Step 2: Find Points for 3x + y = 14
If x = 0,
y = 14 → (0, 14)

If x = 2,
y = 14 − 6 = 8 → (2, 8)

If x = 4,
y = 14 − 12 = 2 → (4, 2)

Plot these points and join them to get a straight line.

Step 3: Plot Second Equation
Second equation:
y = 2

This is a horizontal line parallel to the x-axis passing through y = 2.

Step 4: Find Point of Intersection
The lines intersect where y = 2.

Substitute y = 2 into first equation:
3x + 2 = 14
3x = 12
x = 4

So intersection point = (4, 2)

Final Answer:
x = 4
y = 2