Question

Generalize A system of linear equations has exactly one solution. What can you say about the slopes of the lines when the equations are graphed? How do you know? Generalize A system of linear equations has exactly one solution . What can you say about the slopes of the lines when the equations are graphed ? How do you know ?​

Answer 1

If a system of linear equations has exactly one solution then the slopes of both the lines should be different.

Given A system of linear equations has exactly one solution.

Linear equation is a type of equation  when when plotted on the graph gives a straight line. The slope is the ratio of the vertical change to the horizontal change between two distinct points on a line.

let two equations be who have one solution

2x+3y=7

5x+6y=1

solving them

x=7-3y/2

put the value of x in second equation

5(7-3y)/2+6y=1

35-15y/2+6y=1

35-15y+12y=2

-3y=-33

y=11

put the value of y in x=7-3y/2

x=7-3*11/2

x=7-33/2

x=-26/2

x=-13.

There is only one solution which is (-13,11)

Taking equations and convert them into standard form

first

y=7/3-2/3x

second

y=1/6-5/6x

The standard form is y=a+bx where b is slope

from the above equations we can find that the slope of first equation is -2/3 and the slope of second equation is -5/6. In this way we are able to conclude that slopes should be different for one solution.

Learn more about slope here brainly.com/question/3493733

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