ALGEBRA/EQUATION

Solve the following system of equations.

x + 2y = 5
x = 2 - 2 y;

For the first equation, I canceled out the x and divided by 2 on both sides. So y = 5 - x/ y.
For the second equations, this is what I got. x = 2 -2 y / Y = 2 - x/ 2. Thank you so much.

1. 👍 0
2. 👎 0
3. 👁 125
1. When we have a system of linear equations, it can fall into one of three cases:
1. no solution,
2. a unique solution, and
3. an infinite number of solutions.

I am not sure which level of linear algebra you are working on, but I will explain it in the easiest terms:

1. happens when the equations are inconsistent, or contradictory, for example:
x + 2y = 5
x + 2y = 2
The left hand sides are identical, and the right hand sides are different, which is impossible. So we say that there is no solution.

2. happens most of the time when there is a unique solution.
For example:
2x+y=3
x+2y=3
If you solve the system of equations, x=1, y=1. No other values will satisfy both equations.

3. happens when there are more unknowns than equations, so the solution is based on some "assumed values" of arbitrary variables of our choice, called free variables. This way, there is an infinite number of solutions, depending on the choice of the values of the free variables.
Example:
2x+y=6
If we take y as the free variable, then we have:
x=(6-T)/2
y=T
where T can take on any finite value, and the equation will be satisfied.

Decide on which case the given equations fall, and post your answer for checking if you wish.

1. 👍 0
2. 👎 0
2. I would say it falls under the category of number 2. I'm trying. What do you think?

1. 👍 0
2. 👎 0
posted by Amy
3. Have you tried to rearrange the equations to the form where variables are on the left of the equal sign, and the constant terms on the right? Perhaps it will help you see better.

1. 👍 0
2. 👎 0

Similar Questions

1. Math

I cannot come up with the right answers for my matrix. I need to write as a system of equation and solve the system. 1 2 3 x 1 1 1 1 y = 12 -1 1 2 z 2 The answers I come up with are 31 15 15 when I check these, they will not work,

asked by Lynn on April 23, 2008
2. ap government and politics

hi. my teacher assigned us 20 questions and i got most of them, but i couldn't find the answers to these 4 questions. i did try google but it didn't help much. could someone please help me? List and explain how Congress carries

asked by Anonymous on May 6, 2012
3. Psy 285

Discuss how confirmation bias can influence perceptions and how some beliefs can actually generate their own confirmation

asked by Anonymous on February 17, 2011
4. spy

Discuss how confirmation bias can influence perceptions and how some beliefs can actually generate their own confirmation Provide relevant examples to support your explanation. Need some helps.

asked by rose on October 30, 2008
5. Algebra 2

Solve each system. x-4y-6z=-34 -7x+5y-7z=-24 z=5x-7y+18 These are my answers below but I know that they are wrong: x=-3894 y=-112852 z=-107,509,144 I have tried to solve this system probably 10 times, and still not getting an

asked by Taylor on January 29, 2016
6. Social Psychology

Discuss how confirmation bias can influence perceptions and how some beliefs can actually generate their own confirmation in 200 to 300 words. Provide relevant examples to support your explanation.

asked by Mandy on February 18, 2011
7. math

A hotel gives every customer who makes a reservation a confirmation code. How many different confirmation codes can be created if each code has 4 letters followed by 2 numbers?

asked by Jessie on February 26, 2017
8. Math

Determine which system below will produce infinitely many solutions. A.-6x+3y=18 4x-3y=6 B.2x+4y=24 6x+12y=36 C.3x-y=14 -9x+3y=-42 D.5x+2y=13 -x+4y=-6 Solve the system of equations. x + 3y = −1 2x + 2y = 6 A.(-4,1) B.(2,-1)

asked by Juliet on December 2, 2015
9. Math Check

Hi! Can someone check my answers? Thanks! Directions: Solve each system by using the elimination method. Make sure to write your answer in (x,y) form. 1.) 3x-5y=2 2x+5y=13 2.) 3x+11y=4 -2x-5y=9 My answers: 1.) (3,7/5) 2.) (-17,5)

asked by Heather on March 4, 2015
10. social PSY

I need some help with this assignment. I really don't understand this class. Can someone please help me understand it better...thanks! Discuss how confirmation bias can influence perceptions and how some beliefs can actually

asked by Mandy on February 20, 2011

More Similar Questions