from the 2nd:
y = 3x - 1
then
6x^2+3y^2-111x-y+128=0
6x^2 + 3(3x - 1)^2 - 111x - (3x - 1) + 128 = 0
simplify, and solve the equation.
(comes apart nicely)
solve each system of equations
6x^2+3y^2-111x-y+128=0
3x-y=1
2 answers
6x^2+3y^2-111x-y+128=0 , 3x-y=1
3 x - y = 1
Subtract 3x to both sides:
- y = 1 - 3 x
- y = - 3 x + 1
Multiply both sides by - 1
y = 3 x - 1
plug y = 3 x - 1 into 6 x² + 3 y² -111 x - y +128 = 0
6 x² + 3 ∙ ( 3 x - 1 )² -111 x - ( 3 x - 1 ) + 128 = 0
6 x² + 3 ∙ ( 9 x² - 6 x + 1 ) - 111 x - 3 x + 1 + 128 = 0
6 x² + 27 x² - 18 x + 3 - 111 x - 3 x + 1 + 128 = 0
33 x² -132 x + 132 = 0
Divide both sides by 33
x² - 4 x + 4 = 0
Solution of this equation:
x = 2
y = 3 x - 1 = 3 ∙ 2 - 1 = 6 - 1 = 5
Solution x = 2 , y = 5
( 2 , 5 )
3 x - y = 1
Subtract 3x to both sides:
- y = 1 - 3 x
- y = - 3 x + 1
Multiply both sides by - 1
y = 3 x - 1
plug y = 3 x - 1 into 6 x² + 3 y² -111 x - y +128 = 0
6 x² + 3 ∙ ( 3 x - 1 )² -111 x - ( 3 x - 1 ) + 128 = 0
6 x² + 3 ∙ ( 9 x² - 6 x + 1 ) - 111 x - 3 x + 1 + 128 = 0
6 x² + 27 x² - 18 x + 3 - 111 x - 3 x + 1 + 128 = 0
33 x² -132 x + 132 = 0
Divide both sides by 33
x² - 4 x + 4 = 0
Solution of this equation:
x = 2
y = 3 x - 1 = 3 ∙ 2 - 1 = 6 - 1 = 5
Solution x = 2 , y = 5
( 2 , 5 )
1 answer