3 l inearquestions and need some advice please!

[hello_kitty]

For a question like:   y – 6 = -1/4(x+5)
Is it better to multiply the 4 onto the L.H.S OR expand the brackets??

Silly question, but, Why do we solve simultaneous equations?
Is it to solve the point of intersection, when the equation is true/same?


Questions
1) A shopkeeper sold his entire stock of shirts and ties in a sale for $10 000. The shirts were priced at 3 for $100 and the ties $20 each. If he had sold only half the shirts and two thirds of the ties he would have received $6000. How many of each did he sell in the sale? State variables.

Answer120 shirts, 300 ties

Anne and Maureen live in towns that are 57km apart. Anne sets out at 9am one day to ride her bike to Maureen’s town at a constant speed of 20km/h. At the same time Maureen sets out to ride to Anne’s town at a constant speed of 18km/h.
a)   Write down a rule for the distance (d km), that h of them is from Anne’s place at a time t minutes after 9am


Given that the lines 4x -3y =10 and 4x –ly =m are perpendicular and intersect at the point (4,2). Find values of l and m.

Answer: L = -16/3  m = 80/3

Using Substitution in Factorising
X^4 +5x^2 + 6

Answer(x^2 + 3) (x^2 + 2)

[Water]

a) Multiply by -4 on both sides. Easier, common sense




Questions
1) A shopkeeper sold his entire stock of shirts and ties in a sale for $10 000. The shirts were priced at 3 for $100 and the ties $20 each. If he had sold only half the shirts and two thirds of the ties he would have received $6000. How many of each did he sell in the sale? State variables.





100  x 1/3x    + 20  x  y   = 10,000

(1/2) 100 x 1/3x   + (2/3) 20 x y = 6000





2) I don't get the question




3) Find such that gradients of both equations, when multiplied against one another is -1...

So, first you have to manipulate your equations to find the gradient of your first one.

Then find the number coefficient of y in your second equation, such that it can create your second gradient, when multiplied by the 1st to be -1.  You can find your m, through the intersection point afterwards



4) Let y = x^2


Therefore,


your equation can be shifted to turn into y^2 + 5y + 6. After that, normal quadratics, then replace it with x^2=y again.


This will constitute, your answer