Good Day,
How can I solve the following system of equations? I suppose I'm having trouble with the x and y placed together in the middle term.
3x^2+4xy+5y^2=8
x^2+3xy+2y^2=0
Thank you, if you would not mind showing all of your work-as I would like to be able to finish the set of problems similar to this one!!
How can I solve the following system of equations? I suppose I'm having trouble with the x and y placed together in the middle term.
3x^2+4xy+5y^2=8
x^2+3xy+2y^2=0
Thank you, if you would not mind showing all of your work-as I would like to be able to finish the set of problems similar to this one!!
-
x² + 3xy + 2y² = 0
(x + y)(x + 2y) = 0
x = -y
or
x = -2y
-------------------------
x = -y
3x² + 4xy + 5y² = 8
3(-y)² + 4(-y)y + 5y² = 8
3y² - 4y² + 5y² = 8
4y² = 8
y² = 2
y = √2
or
y = -√2
-------------------------
x = -2y
3x² + 4xy + 5y² = 8
3(-2y)² + 4(-2y)y + 5y² = 8
12y² - 8y² + 5y² = 8
9y² = 8
y² = 8/9
y = 2√2/3
or
y = -2√2/3
-------------------------
So all four solutions are
x = -√2, y = √2
x = √2, y = -√2
x = -4√2/3, y = 2√2/3
x = 4√2/3, y = -2√2/3
-
(x + y)(x + 2y) = 0
x = -y
or
x = -2y
-------------------------
x = -y
3x² + 4xy + 5y² = 8
3(-y)² + 4(-y)y + 5y² = 8
3y² - 4y² + 5y² = 8
4y² = 8
y² = 2
y = √2
or
y = -√2
-------------------------
x = -2y
3x² + 4xy + 5y² = 8
3(-2y)² + 4(-2y)y + 5y² = 8
12y² - 8y² + 5y² = 8
9y² = 8
y² = 8/9
y = 2√2/3
or
y = -2√2/3
-------------------------
So all four solutions are
x = -√2, y = √2
x = √2, y = -√2
x = -4√2/3, y = 2√2/3
x = 4√2/3, y = -2√2/3
-