Question

A system of equations is given below. -3x + 6 and y = 6 - 3x

Which of the following statements best describes the two lines?

They have different slopes and different y-intercepts, so they have no solution. They have different slopes and different y-intercepts, so they have one solution. They have the same slope and the same y-intercept, so they have no solution. They have the same slope and the same y-intercept, so they have infinitely many solutions.

Answer 1

They have different slopes and different y-intercepts, so they have no solution

Explanation:

Answer 2

Infinite solutions Answer explained below

Explanation:

Let us see the various conditions for intersections of two lines in simplest way.

1. Same slope and same y intercept : Infinite solutions

2. Same slope and different y intercepts : No solution

3. Different slope and same y intercept : unique solution

4. Different slope and different y intercept : Unique solution

Here slope means the tangent of the angle line makes with the positive x axis and y intercept is the y coordinate at which the line intersect the y axis.

In our equations , we our slopes and y intercepts as

y=-3x+6

slope = -3 and y intercept = 6

y=6-3x

slope = -3 and y intercept = 6

Hence same slope and same y intercept , thus have infinite solutions