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

AI Thread Summary
To solve the simultaneous equations x^2 + y^2 = 10 and y = 2x - 5, start by substituting y in the first equation with the expression from the second equation. This leads to x^2 + (2x - 5)^2 = 10. Expanding the squared term results in a quadratic equation that can be simplified and solved for x. Once x is determined, substitute back to find the corresponding y values. This method effectively eliminates y and allows for solving the equations systematically.
Haroldingo
Messages
38
Reaction score
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..
 
Physics news on Phys.org
If y = 2x - 5 , what is y2 ?
 
SammyS said:
If y = 2x - 5 , what is y2 ?
(2x - 5) 2 ?
 
Haroldingo said:
(2x - 5) 2 ?
Now replace y2 in the first equation with this expression, and solve the resulting quadratic.
 

Thread 'Finding the number of ways to arrange identical balls in a circle (3 different colors)'

I tried to combine those 2 formulas but it didn't work. I tried using another case where there are 2 red balls and 2 blue balls only so when combining the formula I got ##\frac{(4-1)!}{2!2!}=\frac{3}{2}## which does not make sense. Is there any formula to calculate cyclic permutation of identical objects or I have to do it by listing all the possibilities? Thanks
View full post »

Thread 'Greatest possible value of a constant in polynomial'

Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks
View full post »

Similar threads

Solve these simultaneous equations that involve vectors
Replies
6
Views
2K
Solve the simultaneous equations involving x, y, and their squares
Replies
2
Views
1K
Solve the given simultaneous equations in x^2, x and y
Replies
1
Views
1K
Question about this technique for solving simultaneous equations
Replies
4
Views
1K
Find integer points on this equation
Replies
8
Views
1K
Solve the given simultaneous equation
Replies
32
Views
2K
Solve ##\dfrac{3x-6}{5-x}+\dfrac{11-2x}{10-4x}=3\dfrac{1}{2}##
Replies
3
Views
2K
How to Predict Outcomes of New Equations Without Solving for Variables?
Replies
18
Views
3K
Understanding the Trajectory Equation: X^2+Y^2=5
Replies
7
Views
1K
Solving these Simultaneous Equations
Replies
3
Views
2K

Hot Threads

Recent Insights

Back
Top