SOLUTION: solve this simultaneous equation: x+y=10 y=3x²-2x-3 I have tried every way i can think of to solve this equation but i have failed. Please help me

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: solve this simultaneous equation: x+y=10 y=3x²-2x-3 I have tried every way i can think of to solve this equation but i have failed. Please help me      Log On


   

Question 224914: solve this simultaneous equation:
x+y=10
y=3x²-2x-3
I have tried every way i can think of to solve this equation but i have failed. Please help me
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
solve this simultaneous equation:
x%2By=10 Equation 1
y=3x%5E2-2x-3 Equation 2

Step 1. In Equation 1, solve for y=10-x and substitute y into Equation 2.

10-x=3x%5E2-2x-3

Step 2. Add x-10 to both sides of the equatiion

10-x%2Bx-10=3x%5E2-2x-3%2Bx-10

0=3x%5E2-x-13

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=3, b=-1, and c=-13

Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 3x%5E2%2B-1x%2B-13+=+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=%28-1%29%5E2-4%2A3%2A-13=157.

Discriminant d=157 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--1%2B-sqrt%28+157+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-1%29%2Bsqrt%28+157+%29%29%2F2%5C3+=+2.25499401435694
x%5B2%5D+=+%28-%28-1%29-sqrt%28+157+%29%29%2F2%5C3+=+-1.92166068102361

Quadratic expression 3x%5E2%2B-1x%2B-13 can be factored:
3x%5E2%2B-1x%2B-13+=+3%28x-2.25499401435694%29%2A%28x--1.92166068102361%29
Again, the answer is: 2.25499401435694, -1.92166068102361. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B-1%2Ax%2B-13+%29



Step 4. Now, for each value of x found in Step 3, substitute into y=10-x to get two values for y.

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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