Solving a quadratic in two variables

In summary, the conversation discusses solving a quadratic equation with coefficients a, b, c, d, e, and f for y in terms of x. It is stated that the final term should be f instead of c. The possibility of solving for y using algebra is mentioned, with the understanding that the resulting coefficients will include x and x^2. The conversation ends with a clarification on what is meant by "solving for y".
  • #1
zzmanzz
54
0

Homework Statement



Hi,

If I have an equation in the form

0 = a*x^2 + b*y^2 + c*x*y + d*x + e*y + c

Is it possible to solve this for y? Was hoping just to get a helpful link as this isn't for homework - just a personal project.
 
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  • #2
zzmanzz said:

Homework Statement



Hi,

If I have an equation in the form

0 = a*x^2 + b*y^2 + c*x*y + d*x + e*y + c

Is it possible to solve this for y? Was hoping just to get a helpful link as this isn't for homework - just a personal project.

I assume you really mean ##0 = a x^2 + b y^2 + c x y + d x + e y + f##; that is, that the last term should not be ##c## as you wrote.

Yes, you can easily solve for ##y## in terms of ##x##, because it is a quadratic equation of the form ##A y^2 + B y + C = 0##, where you can use algebra to figure out what are ##A, B## and ##C## in terms of ##a,b,c,d,e,f## and ##x##.
 
  • #3
Ahh makes sense.. so the new A,B, C terms will have X, X2 in it.. but that's ok since I have the other coefficients. Thanks!
 
  • #4
What do you exactly mean by solve for y?
 

1. What is a quadratic equation in two variables?

A quadratic equation in two variables is an equation that contains two variables, usually represented as x and y, and has the form ax2 + bx + cy + d = 0, where a, b, c, and d are constants. This type of equation can be graphed as a parabola and has multiple solutions, or points where the equation is true.

2. How do you solve a quadratic equation in two variables?

To solve a quadratic equation in two variables, you can use the same methods as you would for a regular quadratic equation with one variable. This includes factoring, completing the square, or using the quadratic formula. However, when solving for two variables, you must find values for both variables that make the equation true.

3. What is the purpose of solving a quadratic equation in two variables?

Solving a quadratic equation in two variables can help find the solutions or points of intersection between two equations. This can be useful in solving real-world problems involving multiple variables, such as finding the maximum or minimum value of a function or determining the break-even point in a business scenario.

4. Can a quadratic equation in two variables have more than one solution?

Yes, a quadratic equation in two variables can have more than one solution. This is because the equation represents the points where the two variables intersect, and there can be multiple points where this occurs. These solutions can also be real numbers or complex numbers, depending on the values of the variables and constants in the equation.

5. How do you graph a quadratic equation in two variables?

To graph a quadratic equation in two variables, you can first rewrite the equation in the form y = mx + b, where m and b are constants. Then, you can plot points on a coordinate plane by choosing values for x and solving for y. This will create a curved line, or parabola, on the graph. You can also use a graphing calculator or software to graph the equation for you.

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