Simultaneous Equations

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January 25th 2009, 09:53 AM
Mathtard

Simultaneous Equations

Hey guys, I have these two questions, which I am confused about. If anyone could help me I would be very grateful!

"Solve the following simultaenous equations using an analytical method (either elimination or by substitution of methods) and then check your answers by plotting their graphs on the same set of axes.
$<br /> y = 2 + 2x$

$3y = 20 - x$

________________________

second question

Find the roots of the following Quadratic equations using the methods specified:

$x^2 - 6x + 9 = 0$ by Factorisation

$3x^2 - 8x + 2 = 0$ using the quadratic solution formula.
January 25th 2009, 10:37 AM
TheMasterMind

Quote:

Originally Posted by Mathtard

Hey guys, I have these two questions, which I am confused about. If anyone could help me I would be very grateful!

"Solve the following simultaenous equations using an analytical method (either elimination or by substitution of methods) and then check your answers by plotting their graphs on the same set of axes.
$<br /> y = 2 + 2x$

$3y = 20 - x$

________________________

second question

Find the roots of the following Quadratic equations using the methods specified:

$x^2 - 6x + 9 = 0$ by Factorisation

$3x^2 - 8x + 2 = 0$ using the quadratic solution formula.

1.

y=2+2x

3y=20-x

use substitution it is easiest method here

3(2+2x)=20-x

6+6x=20-x

7x=14

x=14div7

x=2

sub back into original to get y

y=2+2(2

y=2+4

y=6

therefore they intersect at (2,6)

check it yourself

2.

I) (x-3)(x-3)

II) use $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

where a=3,b=-8 and c=2
January 25th 2009, 10:46 AM
Mathtard

Thank you very much for your help, I understand this alot better now. Thank you!!!