For which value(s) of parameter m is there a solution for this system { <mtable columna

Alani Conner 2022-05-23 Answered
For which value(s) of parameter m is there a solution for this system
{ m x + y = m m x + 2 y = 1 2 x + m y = m + 1
when does this system of equations have a solution?
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Answers (2)

ryancameron52
Answered 2022-05-24 Author has 8 answers
Compute the values of x and y dependent on m for the following system, then solve 2 x + m y = m + 1 (the last equation) to find the values of parameter m for x and y:
{ m x + y = m m x + 2 y = 1
So,
{ 2 m x + 2 y = 2 m m x + 2 y = 1
Subtracting two equations, will have:
m x = 2 m 1
- If m 0, we may divide by m and get x = ( 2 m 1 ) / m and y = 1 m.
- If m = 0, the system has no solution.
Putting x and y in the last equation m 0, we'll have:
m 3 3 m + 2 = 0
( m 3 1 ) 3 m + 3 = 0
( m 1 ) ( m 2 + m + 1 ) 3 ( m 1 ) = 0
( m 1 ) ( m 2 + m 2 ) = 0
Thus the values of parameter m are m = 1 or m = 2.
Not exactly what you’re looking for?
Ask My Question
ownerweneuf
Answered 2022-05-25 Author has 1 answers
Comment to expert's answer. Be careful: If m = 0 then the equation m x = 2 m 1 gives you 0 = 1, so you have no solution. Ruling out this case you have x = 2 m 1 m or ( 2 m 1 ) / m which is not th esame as 2 m 1 / m.
Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Relevant Questions

asked 2022-04-04

Solve for the variables b and c in the system of equations:
{6b+2c=26b+4c=3

asked 2022-04-27

Solve the system by substitution.
x-4y=-8
5y-1=x

asked 2021-08-09
x+y=2x+2y=11
3x+3y=62x+4y=22
x+y=2x+2y=11
3x+3y=62x+4y=22
Two systems of equations are shown. Which TWO of the following statements each provide sufficient reasoning to show that the systems have the same solution?
The two equations in the second system are multiples of the two equations in the first system. A)
The two constant terms in the second system are multiples of the two equations in the first system. B)
The graphs of the equations in the first system coincide with the graphs of the equations in the second system. C)
The slopes of the graphs of the equations in the first system are equivalent to the slopes of the graphs of the equations in the second system. D)
The x -intercepts of the graphs of the equations in the first system coincide with the x -intercepts of the graphs of the equations in the second system. E)
asked 2022-06-01
How to solve this sytem of equation:
{ ( a 2 + 4 + a ) ( b 2 + 1 + b ) = 1 27 a 6 + 8 b = a 3 + 2
I tried to analysis equation (1):
a 2 + 4 + a = b 2 + 1 b a + b = b 2 + 1 a 2 + 4
4 a 2 + 16 b 2 + 20 a b = 9
And then, I don't know how to solve this.
asked 2021-02-12
Manuel has $54 to buy CDs and books. Each CD costs $9, and each book costs $6. He wants to buy exactly 7 items to spend all of his money. Write a system of equations that could be solved to determine the number of CDs and the number of books Manuel buys.
asked 2022-06-02
System of 3 equations
1 x + 1 y + z = a 1 y + 1 x + z = b 1 z + 1 x + y = c
asked 2022-05-22
how to resolve this system of differential equations of order 1?
{ p ˙ 1 = 1 z p 2 p 3 p ˙ 2 = 1 z p 1 p 3 p ˙ 3 = ( 1 y 1 x ) p 1 p 2
where p 1 ( 0 ) = a , p 2 ( 0 ) = b , p 3 ( 0 ) = c and x , y , z are constants.
1) how to resolve this system differential equations by hand?
2) what if x = y = M where M is a constant?