Question

A system of equations is shown below.

y = 1.5x - 3
y = 1.5x + 4

Which statement is true about the system
A the system has no solution
B the solution has infinitely many soulutions
C the system has exactly one solution and it’s (0,-3)
D the system has exactly one solution and it’s (6,4)

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.