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

$3y=\dfrac{3}{2}x+6$

$\dfrac{1}{2}y-\dfrac{1}{4}x=3$

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,

$3y=\dfrac{3}{2}x+6$               ...(i)

$\dfrac{1}{2}y-\dfrac{1}{4}x=3$            ...(ii)

Rewritten the given equation in slope intercept forms.

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

$y=\dfrac{1}{2}x+2$

Slope of this line is $\dfrac{1}{2}$ and y-intercept is 2.

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

$y-\dfrac{1}{2}x=6$

$y=\dfrac{1}{2}x+6$

Slope of this line is $\dfrac{1}{2}$ 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.