Solve the system of equations algebraically: y=x^2+4 y=2x+7

Expert Answers

An illustration of the letter 'A' in a speech bubbles

Given:-

y = (x^2) + 4...........(1)

y = 2x + 7...........(2)

Putting the value of 'y' from (2) into (1) we get

2x + 7 = (x^2) + 4

or, (x^2) - 2x - 3 = 0

or, (x^2) - 3x + x - 3 = 0

or, x(x-3) + (x-3) = 0

or,  (x+1)*(x-3) = 0

Thus, either x= -1   which gives y = 5

or, x = 3 which gives y = 13

Approved by eNotes Editorial Team

Posted on

An illustration of the letter 'A' in a speech bubbles

We have to solve the system of equations:

y=x^2+4

y=2x+7

Equate the value of y

=> x^2+4 = 2x+7

=> x^2 - 2x - 3 = 0

solving the quadratic equation we get two values of x.

=> x^2 - 3x + x - 3 = 0

=> x(x - 3) + 1(x - 3) = 0

=> (x - 3)(x + 1) = 0

Or x = 3 and x = -1

For x = 3, y = 2x + 7 = 13

For x = -1, y = 2x + 7 = 5

Therefore the required solution is

( 3 , 13) and ( -1 , 5)

Approved by eNotes Editorial Team

Posted on

Soaring plane image

We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

  • 30,000+ book summaries
  • 20% study tools discount
  • Ad-free content
  • PDF downloads
  • 300,000+ answers
  • 5-star customer support
Start your 48-Hour Free Trial