Solving systems of nonlinear equations Quiz 1

Question 1

Choose the correct value of $$l$$ and $$m$$ if both variables are related with the nonlinear equation and there exists the solution. $$  l = {m^2} - 5 \  l = 2m - 2 \  $$

Accepted Answer

$$( - 1, - 4),(3,4)$$

Answer

$$(2,4),(3,4)$$

Answer

$$( - 2, - 4),(6,4)$$

Answer

$$(2,1),(3,8)$$

Question 2

The $$p$$ and $$q$$ variables choose the appropriate points for the following system of nonlinear equations. $$ \  - p + q = 3 \  pq =  - 2 $$

Accepted Answer

$$(p,q) = ( - 1,2)\,\,or\,\,( - 2,1)$$

Answer

$$(p,q) = ( - 1,2)\,\,or\,\,( - 2, - 1)$$

Answer

$$(p,q) = ( - 1, - 2)\,\,or\,\,( - 2,1)$$

Answer

None of the above

Question 3

Following a System of nonlinear equations that possesses two variables, choose them if there exist two solutions. $$r + 2s = 3 \ {r^2} + 3rs = 10$$

Accepted Answer

$$r = 4	ext{ and } s =  - 0.5\,\,Or\,\,r = 5	ext{ and } s =  - 1$$

Answer

$$r = 4	ext{ and } s = 0.5\,\,Or\,\,r = 5	ext{ and } s = 1$$

Answer

$$r = 4	ext{ and } s = 0.5\,\,Or\,\,r = 5	ext{ and } s =  - 1$$

Answer

$$r = 4	ext{ and } s =  - 0.5\,\,Or\,\,r =  - 5	ext{ and } s =  - 1$$

Question 4

The following system of the equation has a consistent solution then choose the correct points for the system.$$ p^2 - q^2=7$$  $$2q = 2 + p$$

Accepted Answer

$$(p,q) = ( - 2.66, - 0.33)\,\,or\,\,(4,3)$$

Answer

$$(p,q) = ( - 2.65,0.17)\,\,or\,\,(4.65,3.82)$$

Answer

$$(p,q) = ( - 3.03,1.48)\,\,or\,\,(7.033,6.517)$$

Answer

None of the above

Question 5

Suppose there are two-variable systems shown in matrix format, choose the correct possible combination pair for the solution that exists. $$ \ \left[ {\begin{array}{*{20}{c}}  1&2 \   3&{ - 2} \end{array}} ight]\left[ {\begin{array}{*{20}{c}}  {{x^2}} \   {{y^2}} \end{array}} ight] = \left[ {\begin{array}{*{20}{c}}  {11} \   {25} \end{array}} ight]$$

Accepted Answer

$$(3,1),\,( - 3, - 1),\,( - 3,1),\,(3, - 1)$$

Answer

$$(1,3),\,( - 1,1),\,( - 1,3),\,( - 1, - 1)$$

Answer

$$(3,1),\,( - 3,1),\,(3, - 1),\,( - 3, - 3)$$

Answer

$$(1,3),\,( - 1, - 1),\,(1, - 3),\,( - 1, - 1)$$