Question #f5d8c

4 Answers
Dec 7, 2017

Solution : p=-6 , r=12.5 and p=3 , r=-1 p=6,r=12.5andp=3,r=1

Explanation:

3p+2r=7(1) and p^2-2r=11(2) 3p+2r=7(1)andp22r=11(2). From equation(1)

we get 2r= 7-3p 2r=73p Putting 2r= 7-3p 2r=73p in equaition (2)

we get p^2-(7-3p)=11or p^2+3p-7=11 p2(73p)=11orp2+3p7=11 or

p^2+3p-7-11=0 or p^2+3p-18=0p2+3p711=0orp2+3p18=0 or

p^2+6p-3p-18=0 or p(p+6) -3(p+6)=0p2+6p3p18=0orp(p+6)3(p+6)=0 or

(p+6)(p-3)=0 :. p= -6 or p=3

When p=-6 ; 2r = 7- 3*(-6)=7+18 or 2r=25 or

r=12.5 :. Solution: p=-6 , r=12.5

When p=3 ; 2r = 7- 3*3=7-9 or 2r=-2 or

r=-1 :. Solution: p=3 , r=-1

Solution : p=-6 , r=12.5 and p=3 , r=-1 [Ans]

Dec 7, 2017

3p + 2r = 7................[1]

and

p^2 - 2r =11..............[2]

Adding [1] and [2] we get

p^2 +3p-18=0

=> p^2 +6p-3p-18=0

=> p(p +6)-3(p+6)=0

=> (p +6)(p-3)=0

So p= - 6 and 3

Inserting these in [1] we get

3(-6)+2r=7

=>r=25/2=12.5

and

3xx3+2r=7

r=-2/2=-1

So solutions are
p=-6 and r= 12.5

or
p=3and r= -1

Dec 7, 2017

(p,r)to(-6,25/2)" or "(3,-1)

Explanation:

3p+2r=7to(1)

p^2-2r=11to(2)

"from equation "(1)" we can express 2r as"

2r=7-3pto(3)

color(blue)"substitute in "(2)

p^2-(7-3p)=11

rArrp^2-7+3p-11=0

rArrp^2+3p-18=0

"the factors of - 18 which sum to + 3 are + 6 and - 3"

rArr(p+6)(p-3)=0

"equate each factor to zero and solve for p"

p+6=0rArrp=-6

p-3=0rArrp=3

"substitute each value in "(3)" and solve for r"

2r=7-3prArrr=1/2(7-3p)

p=-6tor=1/2(7+18)=25/2rArr(-6,25/2)

p=3tor=1/2(7-9)=-1rArr(3,-1)

Dec 7, 2017

p=3 r=-1

Explanation:

In order to do this problem with simultaneous equations, we must first isolate -2r from the first equation.
3p+2r=7
3p-7=-2r
Now that we have negative 2r, we can substitute it into the second equation.
p^2-2r=11
p^2+(3p-7)=11
Now, let's bring all the variables and constants to one side and solve the equation by factorization.
p^2+3p-18=0
(p+6)(p-3)
p=-6,3
With both of these solutions, plug them into the original equations and solve for r. The only solution that works in this circumstance is if p=3 and r=-1.