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)   (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 (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=26896 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 3, -15.2222222222222. Here's your graph:

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


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