Solving Simultaneous Equations: x^2 + y^2 = 10 and y = 2x - 5

In summary, The conversation is about solving a simultaneous equation by eliminating y. The equations given are x^2 + y^2 = 10 and y = 2x - 5. The attempt at a solution includes trying to make 5 the subject of the equation and squaring it, but these methods do not work. The suggested solution is to replace y^2 in the first equation with the expression (2x - 5)^2 and solve the resulting quadratic equation.
  • #1
Haroldingo
38
1

Homework Statement



Sure I could do this by looking at the mark scheme, but i need to know HOW and WHY, so that in the future i can do these equations by myself. Thanks :)

by elimenating y, solve the simeltaneous equation

Homework Equations



x^2 + y^2 = 10
y = 2x - 5

The Attempt at a Solution



I thought i might have to make 5 the subject for the equation for this to work?

Outside of this my solution was to square it but that didn't work either..
 
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  • #2
If y = 2x - 5 , what is y2 ?
 
  • #3
SammyS said:
If y = 2x - 5 , what is y2 ?
(2x - 5) 2 ?
 
  • #4
Haroldingo said:
(2x - 5) 2 ?
Now replace y2 in the first equation with this expression, and solve the resulting quadratic.
 

FAQ: Solving Simultaneous Equations: x^2 + y^2 = 10 and y = 2x - 5

What are simultaneous equations?

Simultaneous equations are a set of two or more equations that have multiple variables and must be solved at the same time.

What is the purpose of solving simultaneous equations?

The purpose of solving simultaneous equations is to find the values of the variables that satisfy all of the equations at the same time. This can help in finding the intersection points of lines or the common solutions to different equations.

What methods can be used to solve simultaneous equations?

There are several methods that can be used to solve simultaneous equations, including substitution, elimination, and graphing. These methods involve manipulating the equations to eliminate one variable and solve for the others.

Can simultaneous equations have more than two variables?

Yes, simultaneous equations can have any number of variables. However, the number of equations must also match the number of variables in order to solve the system.

What are the real-life applications of simultaneous equations?

Simultaneous equations have many real-life applications, such as in solving problems related to business, finance, and engineering. They can be used to model and solve systems with multiple variables, such as determining the optimal production levels for a company or analyzing the interactions between different factors in a system.

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