SOLUTION: URGENT QUESTION NEEDED BY TOMORROW. hey there.. thankyou soom much..:) great help. the question is
solve.
2x-3y+1=0
x^2 -y^2=7
thank you so much
Question 206575: URGENT QUESTION NEEDED BY TOMORROW. hey there.. thankyou soom much..:) great help. the question is
solve.
2x-3y+1=0
x^2 -y^2=7
thank you so much Answer by nerdybill(7384) (Show Source):
You can put this solution on YOUR website! 2x-3y+1=0 (equation 1)
x^2 -y^2=7 (equation 2)
.
Solve equation 1 for y:
2x-3y+1=0
2x-3y=-1
-3y=-1-2x
3y=1+2x
y = 1/3 + (2x/3)
.
Plug the above into equation 2 and solve for x:
x^2 -y^2=7
x^2 -(1/3 + (2x/3))^2=7
x^2 -(1/3 + (2x/3))(1/3 + (2x/3))=7
x^2 -(1/9 + 2x/9 + 2x/9 + 4x^2/9 )=7
x^2 -(1/9 + 4x/9 + 4x^2/9 )=7
x^2 - 1/9 - 4x/9 - 4x^2/9 =7
9x^2 - 1 - 4x - 4x^2 = 63
5x^2 - 8x - 1 = 63
5x^2 - 8x - 64 = 0
Solving for x using the quadratic equation (see below) gives us:
x = {4.466, -2.866}
.
Plug back into equation 1 to find y:
When x =4.466
2x-3y+1=0
y = 1/3 + (2x/3)
y = 1/3 + (2(4.466)/3)
y = 1/3 + (8.932/3)
y = 1/3 + (8.932/3)
y = 3.311
.
When x =-2.866
2x-3y+1=0
y = 1/3 + (2x/3)
y = 1/3 + (2(-2.866)/3)
y = 1/3 + (-5.732/3)
y = 1/3 + (-1.911)
y = -1.577
.
Our two solutions are then:
(x,y) = (4.466, 3.311)
(x,y) = (-2.866, -1.577)
.
Details of quadratic to follow:
