Question

Systems of equations:

Solve the system of equations algebraically.

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

Answer 1

The solutions to the system of equations are (x, y) = (3, 4) and (x, y) = (3, -4).

Step-by-step explanation:

To solve the system of equations algebraically, we can begin by solving one equation for one variable and then substituting that expression into the other equation.

Let's solve the second equation for x:

3y - 4x = 0

4x = 3y

x = (3/4)y

Now substitute this expression for x into the first equation:

x^2 + y^2 = 25

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

(9/16)y^2 + y^2 = 25

(25/16)y^2 = 25

(25/16)y^2 = 25

y^2 = 400/25

y^2 = 16

y = ±4

Substitute the values of y back into the expression for x:

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

Therefore, the solutions to the system of equations are (x, y) = (3, 4) and (x, y) = (3, -4).