Question

Given that the value of b can never be equal to -1, determine if the equations are intersecting, parallel, or coincident.

x+2y = 6
4x + 8y = 24

Answer 1

The equations are coincident, representing the same line.

Step-by-step explanation:

To determine if the equations are intersecting, parallel, or coincident, we can compare the slopes and y-intercepts of the two equations.

Equation 1: x + 2y = 6

Equation 2: 4x + 8y = 24

We can rewrite both equations in slope-intercept form, y = mx + b.

Equation 1: y = -1/2x + 3

Equation 2: y = -1/2x + 3

Since both equations have the same slope (-1/2) and same y-intercept (3), they are coincident and represent the same line.