SOLUTION: Suppose we have the following linear system: Ax + By = C (1) Dx + Ey = F (2) (a) Write the slope of the line determined by equation (1) (b) Write the slope of

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Suppose we have the following linear system: Ax + By = C (1) Dx + Ey = F (2) (a) Write the slope of the line determined by equation (1) (b) Write the slope of      Log On


   

Question 1048549: Suppose we have the following linear system:
Ax + By = C (1)
Dx + Ey = F (2)
(a) Write the slope of the line determined by equation (1)
(b) Write the slope of the line determined by equation (2)
(c) What must be true about the given coefficients to guarantee that the
system is consistent?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Ax+%2B+By+=+C......... (1)
Dx+%2B+Ey+=+F+........ (2)
(a) Write the slope of the line determined by equation (1)
Ax+%2B+By+=+C.....solve for y
By+=+-Ax+%2BC
y+=+-%28A%2FB%29x+%2BC%2FB
the slope is +-%28A%2FB%29.....restriction:B%3C%3E0
(b) Write the slope of the line determined by equation (2)
Dx+%2B+Ey+=+F+
+Ey+=+-Dx%2BF+
+y+=+-%28D%2FE%29x%2BF%2FE+
the slope is +-%28D%2FE%29.....restriction:E%3C%3E0
(c) What must be true about the given coefficients to guarantee that the
system is consistent?
A consistent system is a system that has at least one solution.
There will be exactly one unique solution if the coefficient of x and y is not 0
means, if +-%28A%2FB%29%3C%3E0 and +-%28D%2FE%29%3C%3E0