x^2 + y^2 = 25... Algebra???

Question

Solve algebraically or graphically!

x^2 + y^2 = 25
3y - 4x = 0

I need help because my notes are chicken scratch and I can't tell by my notes how the hell to do this!

Answer 1

3y = 4x
y = (4/3)x

x² + (16/9)x² = 25
(25/9)x² = 25
x² = 9
x = ± 3

y = ± 4

ANSWER
(3,4) , (- 3 , - 4)

Answer 2

x = 3 and y = 4

Answer 3

Use your second equation to get an expression for y...

3y - 4x = 0
3y = 4x
y = 4x / 3

...then substitute that for y in the first equation

x^2 + y^2 = 25
x^2 + ( 4x / 3 )^2 = 25

Simplify; now you have a quadratic equation in x that is solved using the usual techniques. Once you find the two possible values for x, the second equation gives you the corresponding values of y.

Answer 4

x^2 + y^2 = 25 ............... (1)
3y - 4x = 0 ........................(2)

From eqn (2) we get -
3y = 4x
=> y = (4/3) x
Substitute this value in eqn (1) we get -

x^2 + [ (4/3) x ]^2 = 25
=> x^2 + (16/9) x^2 = 25
=> x^2 [ 1 + 16/9 ] = 25
=> x^2 [ 25/9 ] = 25
=> x^2 = 9
=> x = (+/-) 3
But y = 4/3 x
ie y = 4/3 ( + x ) and also (- x )

ie y = 4/3 ( +/- 3 )
Hence y = + 4 and - 4

Hence Answer is -

when x = 3, y = 4 and when x = - 3, y = - 4

Answer 5

x^2 + y^2 = 25
3y - 4x = 0

you can do this graphically

x^2 + y^2 = 25 is a circle with center at origin and radius =5
and 3y - 4x = 0 is the equation of a line

y = 4x/3

the solution = intersection points of the line with the circle

Answer 6

3y -- 4x = 0 => y = 4x/3
x^2 + y^2 = 25 => x^2 + (4x/3)^2 = 25 => 25x^2 = 225
=> x^2 = 9 => x = 3
then y = 4x/3 = 4(3)/3 = 4
x = 4, y = 3.

Answer 7

3y - 4x = 0

3y = 4x

9y^2 = 16x^2

x^2 + y^2 = 25

9x^2 + 9 y^2 = 225

9x^2 + 16x^2 = 225

25x^2 = 225

x^2 = 9

x = -3 or x = 3

If x = -3, then y = -4.

If x = 3, then y = 4.

So the ordered pair solutions are (-3, -4) and (3, 4).

Answer 8

Well first I would go focus on getting the X or Y isolated on the linear equation so i would turn 3y - 4x = 0 to 3y = 4x
y= 4/3 x
now you plug it in to the other equation
x^2 + (4/3x)^2 = 25
x^2 + 1.77777777x = 25
now you subtract x on 1 side to = 0
x^2 + 1.77x -25 = 0
-1.77 + or - sqrt of 1.77^2 - 4(-25) over 2
4.19 = x

now u can plug it in to the equation
4.19^2 + y^2 = 25
25 - 17.5561 = 7.4439
square root it and you get y =2.73
17.56 + 7.56=25

Answer 9

x^ 2 + y^2 = 25 subtract x^2 to both sides
y^2 = -x^2 + 25 take the square root for both
sides
y = x+5

3y - 4x = 0 add 4x to both sides
3y = 4x now divide 3 to both sides
y= 4/3x

Answer 10

1) The answer is a graph of a circle with the center at the origin (0,0) and a radius of 5.

2) 3y - 4x = 0
3y=4x
y = 4/3 x (0,0) and slope = 4/3 (up 4 and right 3 places) gives the point (3,4)

So, plot (0,0) and (3,4), then draw the line that connects them.