Maths solving simultaneous equations using graphs

[*mystical*]

here is the question:

1.a)draw the graph of x^2 + y^2 = 25 and y = x + 1 on the same grid.

b) Use the graph to solve simultaneously the two equations.

is it allowed to plot the graph (after rearranging the formula) y = square root of 2 - x^2 (there isnt a square root key on the keyboard lol)

please help asap

thanx

xx

[kempie]

Isn't y = √(25-x�) ?

[*mystical*]

o yeh got confused and typed it wrong lol, dat wat i meant, thanx

[stevie21]

If you draw the 2 graphs then it'll give a strong hint as to the answers.
Another approach is to get the 2 equations looking similar and then add or subtract them from each other. I'm sure there's a technical term for this but :
x� + y� = 25 or y� = 25 - x�
and
y=x+1 or y� = (x+1)�
start to look similar, in that you've isolated the y� part.

y� = x� + 2x +1 (which, if you introduce the first equation, is equal to 25-x� )
25 - x� = x� + 2x + 1
0 = 2x� + 2x - 24 (divide by 2)

gives (x+3)(x-4) so x=3 (which makes y=4)
and x= -4 (and thus y=-3)

[kempie]

Nice answer stevie21 but the question asked to solve the simultaneous equations graphically not by substitution.

[*mystical*]

thanx 4 that

but what i really need to do is to plot this on to a graph. is it right when the question asks for the solution for y, not y^2

i came across a problem when one of the equations is y, and the other is y^2, are they allowed on the same graph.

is x^2 + y^2 = 25 a circular graph equation

[kempie]

x� + y� = 25 is a circle centred at the origin, radius = 5

[kempie]

When you have a graph with axes x & y you cannot 'plot' y� as such so you need to rearrange it into the form y = ... so that for every value of x you put into the equation you get the corresponding value for y, with each pair x,y being a point on the graph.

You can also place as many equations as you find practical on one graph.

[*mystical*]

Thanks peeps!!!

ur brill lol