Math revision help (+rep)

[DaveTaylor]

Diagram A Shows the line 2x + y = 12

3a. On the same diagram draw the line x + y = 10 (Explain how you get it please!)
b. Use your diagram to find the solution to the system of equtions 2x + y = 12 and x + y = 10 (Explain how you work it out please!)

and then
4) Solve Algebracically 2x + y = 4
x - 4y = 11
(Explain!)

[Jin]

I cant explain it but this looks like a simultaneous equations question,

Answer to 3

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X = 2 Y=8

[Dudedanny123]

x+y=10. On the graph you need to plot the coordinates so that the x and y coordinate adds up to 10. plot (0,10) (1,9) (2,8) (3,7) and keep going until you get to (10,0) which should give you a diagonal line.

[Jesus-Egg]

3a) x + y = 10 If x=0, y must equal 10, and if y=0, x must equal 10. Therefore the graph is going to be a straight line crossing the axes at (0,10) and (10,0)

3b) The solution is where the lines cross, which is at (2,8), therefore x=2 and y=8

4) Simultaneous equations! There are several ways of doing it, and here's how i would do it:

2x + y = 4 (A)
x - 4y = 11 (B)

rearrange B:
x = 4y + 11 (C)

Sub C into A:

2(4y + 11) + y = 4
8y + 22 + y = 4
9y = 4 - 22
9y = -18
y = -2

Sub y=-2 into C:
x = 4(-2) + 11
x = -8 + 11
x = 3

If you want to check it, you can sub the answers into A to make sure it works