Chapter 5, Problem 15CT

To determine

To find: Whether the given system of equations has one solution, no solution or infinitely many solutions.

Answer to Problem 15CT

The system of equations has NO solution because they are parallel lines.

Explanation of Solution

Given information: 8x+4y=12 and 3y=-6x-15.

Formula used: There are three concepts,

i)If both equations has same slope and same y intercept then they have infinitely many solutions because both represents same line.

ii)If slope of both equations are same but y intercepts are different then they have NO solution because both represents parallel lines.

iii)If slope and y intercepts of both lines are different then they have ONE solution because they are intersecting lines.

Calculation:

  $8x+4y=12$

Solve each equation for y.

Subtract both sides $8x$ .It gives,

  $4y=-8x+12$

Divide both sides by 4.

  $y=-2x+3$

Compare it with $y=mx+b$. Where ‘m’ is slope and ‘b’ is y-intercept.

Slope m=-2

Y-intercept b=3

Now, solve the second equation for ‘y’

  $3y=-6x-15$

Solve for y.

Divide both sides by 3.It gives,

  $y=-2x-5$

Compare it with $y=mx+b$

Slope m =-2

y-intercept b=-3

So, both equations has same slope but different y intercepts then they have NO solution. Because they are parallel lines.