Question

A system of equations is shown below.

Answer 1

Given:

The system of equations is

$y=1.5x-3$

$y=1.5x+4$

To find:

The true statement about the given system of equations.

Solution:

The slope intercept form of a line is

$y=mx+b$

Where, m is the slope and b is the y-intercept.

We have,

$y=1.5x-3$

$y=1.5x+4$

On comparing these two lines with slope intercept form, we get

$m_1=1.5,b_1=-3$

$m_2=1.5,b_2=4$

Since the slopes of the lines are equal but the y-intercepts are different, therefore, the two lines are parallel and the system has no solution.

Therefore, the correct option is A.