Question

What is the solution of this system of linear equations? 3y=3/2x+6 1/2y-1/4x=3 a.(3, 6) b.(2, 1) c.No solution d.Infinite number of solutions

Answer 1

Given:

The system of equations is

`3y=(3)/(2)x+6`

`(1)/(2)y-(1)/(4)x=3`

To find:

The solution of the given system of equations.

Solution:

The slope intercept form of a line is

`y=mx+b`

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

We have,

`3y=(3)/(2)x+6` ...(i)

`(1)/(2)y-(1)/(4)x=3` ...(ii)

Rewritten the given equation in slope intercept forms.

In equation (i), divide both sides by 3.

`y=(1)/(2)x+2`

Slope of this line is
`(1)/(2)` and y-intercept is 2.

In equation (ii), multiply both sides by 2 and isolate y variable.

`y-(1)/(2)x=6`

`y=(1)/(2)x+6`

Slope of this line is
`(1)/(2)` and y-intercept is 6.

Since slopes of both lines are same but the y-intercepts are different, therefore, the lines are parallel and the system of equations have no solution.

Therefore, the correct option is c.