2u + v = 7, uv = 6

Question

simultaneous equation help me..... SORRY I MADE A MISTAKE APOLOGISE

Answer 1

uv = 6

 

2u + v = 7

 

Multiply both sides by u:

 

2u^2 + uv = 7u

 

Substitute 6 for uv:

 

2u^2 + 6 = 7u

 

2u^2 - 7u + 6 = 0

 

u = (7 ± sqrt(49-4*2*6))/(2*2)

 

u = (7 ± 1)/4

 

u = 3/2 or 2

 

v = 6/u = 4 or 3

 

Solutions: (u,v) = (3/2,4) or (2,3)

 

check:

                   (3/2,4) or (2,3)

    uv = 6?      6  √        6  √
2u+v = 7?      7  √        7  √

Answer 2

Hi Rodela;

2u + v = 7, uv = 6

Let's take the second equation and isolate one variable...

uv=6

v=6/u

Let's take the first equation and substitute v with 6/u...

(2u)+(6/u)=7

Let's eliminate annoying fractions and multiply both sides by u...

u[(2u)+(6/u)]=7u

2u²+6=7u

Let's move everything to one side by subtracting 7u from both sides...

2u²-7u+6=7u-7u

2u²-7u+6=0

Let's factor.

For the FOIL...

FIRST must be(2u)(u)=2u²

OUTER and INNER must add-up to -7u and both numbers must be negative to render the sum of -7u and product of +6.

LAST must be (6)(1) or (1)(6) or (2)(3) or (3)(2)...

(2u-3)(u-2)=0

Let's FOIL...

FIRST...(2u)(u)=2u²

OUTER...(2u)(-2)=-4u

INNER...(-3)(u)=-3u

LAST...(-3)(-2)=6

2u²-4u-3u+6=0

2u²-7u+6=0

(2u-3)(u-2)=0

Either or both parenthetical equation(s) must equal zero...

2u-3=0, 2u=3, u=3/2

u-2=0, u=2

 

Let's establish the value of v...

2u + v = 7, uv = 6

Let's begin with the second equation...

u=3/2

uv=6

(3/2)v=6

Let's multiply both sides by 2/3...

(2/3)(3/2)v=6(2/3)

v=12/3=4

 

u=2

uv=6

2v=6

v=3

 

First equation...

2u + v = 7

u=3/2

[2(3/2)]+v=7

3+v=7

v=4

 

u=2

[(2)(2)]+v=7

4+v=7

v=3

 

 

When u=2, v=3

When u=3/2, v=4

Answer 3

 

if you plug numbers in, e.g., u=2 and v=3, you get this:

 

2(2) +3 = 7 (works)

 

2(3) = 6 (works)

 

so u=2, v=3

 

you did not make a mistake--  you do not need to know what uv=6 is to answer this problem