ANSWERS TO MATHS ASSIGNMENT SENT IN BY LATOYA; ANSWERED BY Mr. SEAN FEARON

This is from the topic Algebra

#1 Multiply THE two equations containing unknowns x

eg. eq1. y=2x and eq2. y=3x+7

these are two linear equations that if you multiply you will get a quadratic.

i.e eq1 by eq2 =6x^2+14x this is a quadratic equation.

If you add them the answer is  5x+7 which is still linear.

#2 This one is easy you just have to equate the two equations

eq1. q=3p^2-4p eq2. q=-p^2+24

eq1=eq2 therefore 3p^2-4p=p^2+24

i.e 4p^2-4p-24=0  or p^2-p-6=o if you divide by 4 but this is a quadratic equation you can solve with the formula or any other method suitable to you..

Part B you have to find the in-equations of the three lines  using the f coordinated of the lines i can hardly see the numbers however i think i get the scale right. The coordinates are  

line 1 (0,10) and (5,0) ,line 2( -3,0) and  (0,6) ,line 3 (0,2)

Use the gradient equation to find the gradient and then put if in the equation for a straight line to find the inequalities

y=mx+C

1. line 1 (0,10) and (5,0)  (y2-y1)/(x2-x1)=m, C is where the line cut the y axis you read that from the graph. you use the less than or equal sign (</>/=)depending of where the shaded region is whether it is below or above the line.

2. The maximum occurs at the vertex that give you the largest value when you put the coordinated in the profit equation. so if  P=10x+10y  then  just put  in (x,y) i.e (4,2) , (1,8) and (0,2) The the maximum profit should occur at (1,8).

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