Question

Solve the Equation:
x-3y+1 = 0
x^2 -3 + y^2 =11

Answer 1

To solve the system of equations, you can use the substitution method. After solving quadratic equation, you can find the values of y and substitute them back into the first equation to solve for x.

Step-by-step explanation:

To solve the given system of equations:

x - 3y + 1 = 0

x^2 - 3 + y^2 = 11

You can use the substitution method:

1. From the first equation, solve for x: x = 3y - 1
2. Substitute this value of x into the second equation: (3y - 1)^2 - 3 + y^2 = 11
3. Expand and simplify: 9y^2 - 6y + 1 - 3 + y^2 = 11
4. Combine like terms: 10y^2 - 6y - 13 = 0
5. Solve the quadratic equation: use quadratic formula y = (-b ± √(b^2 - 4ac)) / (2a)
6. Plug in the values: y = (-(-6) ± √((-6)^2 - 4(10)(-13))) / (2(10))
7. Simplify and solve for y: y = (6 ± √(36 + 520)) / 20
8. After finding the values of y, substitute them back into the first equation to solve for x

So, the solution for the system of equations is (x, y) = (3y - 1, y)