WMA11 June 2022

• WMA11/01​​ Edexcel​​ IAL P1 June 2022, Q6 (Simultaneous Equations: Non Linear)

In this question you must show all stages of your working.

Solutions relying on calculator technology are​​ not acceptable.

• Given that​​ 

2xy − 3x2​​ = 50

and​​ 

y − x3​​ + 6x = 0

show that​​ 

2x4​​ − 15x2​​ − 50 = 0

(2)

• Hence solve the simultaneous equations​​ 

2xy - 3x2 = 50 

y - x3 + 6x = 0 

Give your answers in fully simplified surd form.​​ 

(5)

SOLUTION​​ 

a- The equation we are asked to show has no y term in it. This means we need to eliminate the y terms.

Substituting the value of y from the equation y − x3​​ + 6x = 0 into 2xy − 3x2​​ = 50

y - x3+6x=0

y=x3-6x

Lets substitute it in​​ 2xy − 3x2​​ = 50.​​ 

2xy - 3x2 = 50

xx3-6x-3x2=50

2x4-12x2-3x2-50=0

2x4-15x2-50=0 

b-​​ 

Always remember, when the word ‘’hence’’ is used in the question, it means we have to use the answer of prevous part and carry the calculations out for the next part of it.​​ 

2x4-15x2-50=0 

Substituting​​ b=x2

2b2-15b-50=0

2b+5b-10=0

2b2+5=0    b-10=0

b=-52    &    b=10

Substituting back​​ b=x2

x2=-52     &    x2=10

Rejecting because of –ve sign inside the root.​​ 

Now, find the value of y by siubstituting the value of x in any of the parent equation given in the question. We are using here​​ 

y=x3-6x

For​​ x=10   ,

y=  103-610 

y=1010-610

y=410

For​​ x= -10

     y=-103-6-10

y= -1010+610

y=-410

Hence, the solution of simultaneous equation is​​ 

x= 10,  y=410

x= -10,  y= -410