Find the Intersection of the Inequalities x^2+y^2=25 , 3x-4y=0

Problem

x2+y2=25,3*x−4*y=0

Solution

1. Solve the linear equation for one variable.

3*x−4*y=0

3*x=4*y

x=4/3*y

2. Substitute the expression for x into the circle equation.

(4/3*y)2+y2=25

3. Simplify the equation to solve for y

16/9*y2+y2=25

16/9*y2+9/9*y2=25

25/9*y2=25

4. Isolate y2 by multiplying both sides by 9/25

y2=9

y=±3

5. Find the corresponding x values by substituting y=3 and y=−3 back into the linear expression.

x=4/3*(3)=4

x=4/3*(−3)=−4

6. Identify the intersection points as coordinate pairs (x,y)

(4,3),(−4,−3)

Final Answer

x2+y2=25,3*x−4*y=0⇒{(4,3),(−4,−3)}

Want more problems? Check here!