SOLUTION: -5y = +4x + 7 -20x + py = -3 What value of p makes this system inconsistent?

Question 964814: -5y = +4x + 7
-20x + py = -3
What value of p makes this system inconsistent?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
solve for y in both equations and place the solution in slope intercept form of y = mx + b here m is the slope and b is the y-intercept.

first equation is -5y = 4x + 7
divide both sides of the equation by -5 to get:
y = -4/5*x - 7/5
m = -4/5
b = -7/5

second equation is -20x + py = -3
add 20x to both sides to get py = 20x - 3
divide both sides by p to get y = 20x/p - 3/p
m = 20x/p
b = -3/p

for the system to be inconsistent, the lines have to be parallel.
then there is no solution that is common to both lines.

the lines are parallel if their slopes are the same and their y-intercepts are different.

slope of the first line is -4/5
slope of the second line is 20/p

you need to find the value of p that makes -4/5 equal to 20/p

set up the equation of -4/5 = 20/p

cross multiply to get -4p = 100
divide by -4 to get p = 100/-4 which makes p = -25.

when p = -25, the equation of y = 20x/p -3 becomes y = 20x/-25 - 3/25.

simplify this to get y = -4/5 * x - 3/25.

the slope is the same and the y-intercept is different so the lines are parallel.

here's the graph of both equations.

first equation is y = -4/5 * x - 7/5
second equation is y = -4/5 * x - 3/25

the lines are parallel.
they will never intersect.
the system is inconsistent which means that there is no solution.

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