Question 932576: Not every system of linear equations has a single solution. Try to make a sketch of a system of linear equations that does not have a single solution. Compare the equations of these
systems. What is true of their slopes?...y-intercepts?...etc…
Answer by TimothyLamb(4379)   (Show Source):
You can put this solution on YOUR website! a system of linear equations can only have multiple solutions if all of the equations are coincident, in which case the system has infinitely many solutions
---
two linear equations are coincident if their graphs lie on top of each other
---
if two linear equations are coincident they have the same slope and the same y-intercept
---
we can build such a system very easily:
---
invent one linear equation:
---
y = 3x + 5
---
find the slope and y-intercept of this equation:
slope = 3
y-intercept = 5
---
to make another linear equation coincident with the above equation, multiply the above equation by any real number other than 1
---
for example:
---
-2.5*(y = 3x + 5)
-2.5y = -2.5*3x - 2.5*5
-2.5y = -7.5x - 12.5
---
find the slope and y-intercept of the second equation:
---
-2.5y = -7.5x - 12.5
y = (-7.5x - 12.5)/-2.5
y = 3x + 5
slope = 3
y-intercept = 5
---
answer:
if two linear equations have multiple solutions they must have the same slope and the same y-intercept
---
Solve and graph linear equations:
https://sooeet.com/math/linear-equation-solver.php
---
Solve quadratic equations, quadratic formula:
https://sooeet.com/math/quadratic-formula-solver.php
---
Convert fractions, decimals, and percents:
https://sooeet.com/math/fraction-decimal-percent.php
---
Calculate and graph the linear regression of any data set:
https://sooeet.com/math/linear-regression.php
|
|
|
