How do I solve by substitution?
X^2 + Y^2 = 1
-X + �ã 3Y = 0
The answer is X= �ã 3/2
Y= 1/2
S={ (�ã 3/2, 1/2), (-�ã 3/2, -1/2)}
I don't know how to go about solving it.
To solve the given system of equations by substitution, follow these steps:
Step 1: Solve one equation for one variable.
In this case, we can solve the second equation for X:
-X + √3Y = 0
Rearrange the equation to isolate X:
-X = -√3Y
X = √3Y
Step 2: Substitute this value of X into the other equation.
Substitute X = √3Y into the first equation:
(√3Y)^2 + Y^2 = 1
Simplify the equation:
3Y^2 + Y^2 = 1
Combine like terms:
4Y^2 = 1
Divide both sides by 4:
Y^2 = 1/4
Take the square root of both sides:
Y = ±1/2
Step 3: Substitute these values of Y into the expression for X.
Substitute Y = 1/2:
X = √3(1/2)
X = √3/2
So one solution is X = √3/2 and Y = 1/2.
Substitute Y = -1/2:
X = √3(-1/2)
X = -√3/2
So another solution is X = -√3/2 and Y = -1/2.
Thus, the solutions to the system of equations are:
X = √3/2, Y = 1/2
X = -√3/2, Y = -1/2
The solution set is S = {(√3/2, 1/2), (-√3/2, -1/2)}.