math question

1. 3y-4x=0 given
2. 3y=4x addition prop of =
3. (3/4)y=x division prop of =
4. x^2+y^2=25 given
5. [(3/4)y]^2+y^2=25 substitution
6. {[(3y)^2]/[(4)^2]}+y^2=25 distributive prop
7. [(9y^2)/16]+y^2=25 squaring
8. [9y^2)/16]+[(16y^2)/16]=25 multiplying y^2 by 16/16
9. (9y^2+16y^2)/16=25 combination of fractions w/ common denominators
10. 25y^2=25*16 addition, multiplication prop of =
11. y^2=16 division prop of =
12. y=±4 sq root both sides
13. 3y=4x step 2
14. 3(±4)=4x substitution
15. x=±3 division prop of =

answer: y=4, x=3 OR y=-4, x=-3

lindsayfleischer:

solve the following system of equations algebraically or graphically:
x^2+y^2=25
3y-4x=0

Thankyou guest,
That was a fabulous solution. I am really pleased that you posted.
I'd just like to suggest a different way that this could be done. (A graphical way)

first you would need to recognise that x ²+y ²=25 is a circle, centre (0,0) and radius 5
and
3y-4x=0 is a line,
3y=4x
y=4/3 *x
So it goes through (0,0) and has a gradient of 4/3
If you draw the line you may well start at (0,0) then go up 4 places and across 3 places making a second point (3,4)
This makes a right angled triangle where the hypotenuse is 5 units so this must be where the line cuts the circle. Using symmetry the other intersection must be (-3,-4)

I just did this graph to show what I am saying but I initially just did it with a hand sketch.

140104 circle and line.JPG