# Simultaneous Equations

• Jan 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.
$
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.
• Jan 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.
$
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
• Jan 25th 2009, 10:46 AM
Mathtard
Thank you very much for your help, I understand this alot better now. Thank you!!!