SOLUTION: I dont know where to start. Please help me in solving this question Simultaneous equation 3x-4y=5 3x^2-xy-3y^2=21

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Question 167729: I dont know where to start.
Please help me in solving this question
Simultaneous equation
3x-4y=5
3x^2-xy-3y^2=21
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Simultaneous equation
3x-4y=5
3x^2-xy-3y^2=21
--------------
Solve the 1 eqn for y
3x-4y=5
-4y = 5-3x
y = (3/4)x - 5/4
Sub for y into the 2nd eqn
3x^2 - x*((3/4)x - 5/4) - 3*((3/4)x - 5/4)^2 = 21
Now it's all in x
3x^2 - (3/4)x^2 + 5x/4 - 3*((9/16)x^2 - 15x/8 + 25/16 = 21
Multiply by 16
48x^2 - 12x^2 + 20x - 27x^2 + 90x - 75 = 336
9x^2 + 110x - 261 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 9x%5E2%2B110x%2B-411+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28110%29%5E2-4%2A9%2A-411=26896.

Discriminant d=26896 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-110%2B-sqrt%28+26896+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28110%29%2Bsqrt%28+26896+%29%29%2F2%5C9+=+3
x%5B2%5D+=+%28-%28110%29-sqrt%28+26896+%29%29%2F2%5C9+=+-15.2222222222222

Quadratic expression 9x%5E2%2B110x%2B-411 can be factored:
9x%5E2%2B110x%2B-411+=+%28x-3%29%2A%28x--15.2222222222222%29
Again, the answer is: 3, -15.2222222222222. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+9%2Ax%5E2%2B110%2Ax%2B-411+%29

x = 3, y = 1
x = -15 2/9, y = -38/3