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:

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=1344 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 4.46606055596467, -2.86606055596467. Here's your graph:

RELATED QUESTIONS
URGNET QUESTION hey there ... thank you this has been great help..:) The question is-... (answered by stanbon)

URGENT QUESTION NEEDED WITHIN @ DAYS TIME(thank you)the question is_ if y=(kx^2)/sqaure... (answered by nerdybill)

Hey guys this question is still boggling my mind :) You see I have a test coming up... (answered by Fombitz)

Show that the area of an equilateral triangle of side 2x is x^2square3, given that tan 60 (answered by nerdybill)

Please help!! I have a test tomorrow and still don't really understand this no matter how (answered by mukhopadhyay)

I know that there are other questions similar to mine posted, and i have tried to use... (answered by mukhopadhyay)

A survey showed that the ratio of telephones to people in the world was 1:8. Of the... (answered by ankor@dixie-net.com)

Hey, Tutor Thanks for taking the time to help me. I have a few questions about graphing... (answered by ikleyn)

I need help solving this problem. Your efforts and time are well appreciated. Have a... (answered by Alan3354)