Simultaneous equation question

  • Thread starter james_rich
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In summary: That way you always know to put the minus sign with the smaller number.In summary, the conversation discusses solving an equation and confirming the correct answer. The participants clarify that x2 means x squared and proceed to substitute equations and factorize to find the solution. After some discussion, they realize that a mistake was made and the correct answer is (-1, 3) and (1, 1). The conversation ends with the participants expressing gratitude and some advice for solving similar problems in the future.
  • #1
james_rich
23
0
Hey just need my answer to be checked on this problem
just to clarify x2 means x squared!

Solve the following

y = 2 - x
x2 + 2xy = 3

Substitute equations

x2 + 2x(2 - x) = 3
x2 + 4x - 2 x2 = 3
-x2 + 4x - 3 = 0

Factorising

(-x + 1) (x - 3) = 0

so x = -1 and 3
_____________________________________________

as y = 2 - x

y = 2 - 3
= -1

y = 2 + 1
= 3

so the co ordinates for the two roots of this curve will be

(-1, 3) and (3, -1)

is this the right answer? i believe it to be, but my answer books says differently!

Please check my answer.
Thanx in advance!
 
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  • #2
james_rich said:
Hey just need my answer to be checked on this problem
just to clarify x2 means x squared!
Solve the following
y = 2 - x
x2 + 2xy = 3
Substitute equations
x2 + 2x(2 - x) = 3
x2 + 4x - 2 x2 = 3
-x2 + 4x - 3 = 0
Factorising
(-x + 1) (x - 3) = 0
so x = -1 and 3

_____________________________________________
as y = 2 - x
y = 2 - 3
= -1
y = 2 + 1
= 3
so the co ordinates for the two roots of this curve will be
(-1, 3) and (3, -1)
is this the right answer? i believe it to be, but my answer books says differently!
Please check my answer.
Thanx in advance!

You made a small mistake where I highlighted.
 
  • #3
sorry, i still don't understand, i checked what i did, i can't see what's wrong with the bit highlighted!

Can anyone elaborate?
 
  • #4
james_rich said:
sorry, i still don't understand, i checked what i did, i can't see what's wrong with the bit highlighted!
Can anyone elaborate?
I didn't read it all but if your factorization was correct, then x = 1 is a solution and not x = -1.
 
  • #5
i think i see what i have done wrong

the x = 3 is right

but it is -x = -1!

so x = 1

so to start again...

as y = 2 - x
y = 2 - 3
= -1
y = 2 - 1
= 1
so the co ordinates for the two roots of this curve is
(-1, 3) and (1, 1)

Thanx a lot, this is the answer in the book, easy mistake i made i think! bah humbug with the positive and negative signs!

Cheers! I can sleep now!
 
  • #6
Good :smile:
 
  • #7
A word of advice, when you factorise like that it usually helps to have the x^2 coefficient be positive.
 

FAQ: Simultaneous equation question

What is a simultaneous equation?

A simultaneous equation is a mathematical equation that involves two or more unknown variables and has to be solved simultaneously. This means that all the equations have to be satisfied by the same set of values for the variables.

How do you solve a simultaneous equation?

There are several methods for solving simultaneous equations, including substitution, elimination, and graphical methods. The most commonly used method is substitution, where one variable is solved for in terms of the other and then substituted into the other equation to find the value of the remaining variable.

Can you give an example of a simultaneous equation?

One example of a simultaneous equation is:

x + y = 10

2x + 3y = 20

To solve this equation, you can use the substitution method by solving the first equation for x in terms of y (x = 10 - y) and then substituting it into the second equation, resulting in the equation 2(10 - y) + 3y = 20. This can then be simplified to y = 5, and plugging this value back into the first equation gives x = 5.

Why are simultaneous equations important?

Simultaneous equations are important in many fields, such as physics, engineering, economics, and more. They allow us to model and solve real-life problems that involve multiple variables and relationships between them. They are also used in advanced mathematics and are essential for understanding more complex algebraic concepts.

What are some common mistakes when solving simultaneous equations?

Some common mistakes when solving simultaneous equations include incorrect application of the method, forgetting to distribute negative signs, and making errors when solving for one variable in terms of the other. It is essential to check your work and double-check your solutions to avoid these mistakes.

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