What Is The Solution To The System Of Equations? Use The Substitution Method And Show Your Work., -5x+Y= -3, -15x+3y=7, (B)\Texplain What Your Answer

What is the solution to the system of equations? Use the substitution method and show your work.

-5x+y= -3
-15x+3y=7
(b) Explain what your answer in part (a) tells you about the association of the lines in this system.

 

Answer:

(a) The system has no solution for (x, y).

(b) The system is parallel, inconsistent and has no solution because they will never intersect or meet at any point.

Step-by-step explanation:

Part (a): Finding the solution (x, y) if any:

Equation (1):

-5x+y= -3

y = 5x - 3   Equation in slope-intercept form y=mx+

slope (m) = 5

y-intercept (b) = -3

Equation (2):

-15x+3y=7

3y = 15x + 7

3y/3 = 15x/3 + 7/3

y = 5x + 7/3    Equation in slope-intercept form y=mx+

slope (m) = 5

y-intercept (b) = 7/3

Find x, by substitution:

5x - 3 = 5x + 7/3  

5x - 5x = 7/3  + 3

0 = 7/3 + 3/3

0 ≠ 10/3  There is no solution to the system.

The system has the same slope at 5 and different y-intercepts at -3 and 7/3, respectively.

Part (b) Association of lines in system.

The system has no solution. It has the same slope, meaning they the lines represented by the given pair of equations are equidistant from each other,  and different y-intercepts. These are the properties of parallel lines.

Therefore the system is parallel, inconsistent and has no solution because they will never intersect or meet at any point.


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