Math--SYSTEM OF EQUATIONS?

Question

Solve

y = x^2 + 4x + 1
y = 5x + 3



x^2 means x squared or x to the second power

Answer 1

First: both "y" variables are isolated - set both equation to equal each other....

x^2 + 4x + 1 = 5x + 3

Sec: set the equation to equal "0" > subtract 5x from both sides...

x^2 + 4x + 1 - 5x = 5x - 5x + 3
x^2 + 4x + 1 - 5x = 3

*Subtract 3 from both sides...

x^2 + 4x + 1 - 5x - 3 = 3 - 3
x^2 + 4x + 1 - 5x - 3 = 0

*Combine "like" terms...

x^2 + 4x - 5x + 1 - 3 = 0
x^2 - x - 2 = 0

Third: factor the equation...

(x - 2)(x + 1) = 0

*Solve both "x" variables >

1. x - 2 = 0
x - 2+2 = 0 + 2
x = 2

2. x + 1 = 0
x + 1 - 1 = 0 - 1
x = -1

x = 2, -1

*Replace "2" and "-1" with the x-variables in either equation to find the corresponding y-variables...

1. y = 5x + 3
y = 5(2) + 3
y = 10 + 3
y = 13

2. y = 5x + 3
y = 5(-1) + 3
y = - 5 + 3
y = - 2

Solutions: (2, 13) and (-1, -2)

Answer 2

Since two things equal to the same thing are equal to each other, we have 5x + 3 = x^2 + 4x +1. Collecting terms, we get x^2 - x -2 = 0. This has obvious factors (x-2)(x+1), so the roots are x = 2 and x = -1. This gives corresponding y values of 13 and -2.

Answer 3

x² + 4x + 1 = 5x + 3
x² - x - 2 = 0
(x-2)(x+1) = 0

x-2 = 0 or x+1 = 0

i.e. x=2 or x= -1

Answer 4

y = x^2 + 4x + 1
y = 5x + 3
Since both equatios = y, they must = eac other, so
x^2 + 4x +1 = 5x + 3
x^2 - x - 2 = 0
(x - 2)(x + 1) = 0
x-2 = 0
x = 2
x+1 =0
x = -1
So x = 2 and x = -1

Answer 5

Because they are both equal to y simply set the two equations equal to each other.

x^2 +4x +1=5x+5
Bring them all to one side

x^2-x-2=0

x=2 and x=-1

Plug BOTH of these answers into the original equations and you will see that x=1 has to be rejected therefore the answer is x=2 and y=13

Answer 6

use substitution or graph it and find the intersection