SOLUTION: Solve this simultaneous equation: y=5-4x² y+3x=6 Please help

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Question 224915: Solve this simultaneous equation:
y=5-4x²
y+3x=6
Please help
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
Solve this simultaneous equation:
y=5-4x%5E2 Equation 1
y%2B3x=6 or y=6-3x Equation 2

Step 1. Set Equations 1 and 2 to be equal.

5-4x%5E2=6-3x

Step 2. Add 4x%5E2-5 to both sides of the equation

5-4x%5E2%2B4x%5E2-5=6-3x%2B4x%5E2-5

0=4x%5E2-3x%2B1

Step 3. To solve, use the quadratic formula given below

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

where a=4, b=-3, and c=1

Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 4x%5E2%2B-3x%2B1+=+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=%28-3%29%5E2-4%2A4%2A1=-7.

The discriminant -7 is less than zero. That means that there are no solutions among real numbers.

If you are a student of advanced school algebra and are aware about imaginary numbers, read on.


In the field of imaginary numbers, the square root of -7 is + or - sqrt%28+7%29+=+2.64575131106459.

The solution is

Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B-3%2Ax%2B1+%29



Step 4. For each value of x found in Step 3, substitute each value into y=6-3x to get a total of 2 values for y. You now have two points as your solution to these equations. Your solutions will be complex numbers.

I hope the above steps were helpful.

For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J

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