# Thread: Simultaneous Equations.

1. ## Simultaneous Equations.

I was wondering if you could doublecheck this question please:

g) $y=2x$ and $y = 2x^2$
y = 4 and x = 2

How would I do this?

h) $y= 6 - x^2$ and $y = 4x +1$

2. ## Re: Simultaneous Equations.

Originally Posted by JibblyJabbly
I was wondering if you could doublecheck this question please:

g) $y=2x$ and $y = 2x^2$
y = 4 and x = 2

no

How would I do this?

h) $y= 6 - x^2$ and $y = 4x +1$

g)

$2x = 2x^2$

$2x - 2x^2 = 0$

$2x(1 - x) = 0$

$x = 0$ and $x = 1$

h)

$6-x^2 = 4x+1$

$0 = x^2 + 4x - 5$

factor and use the zero product property to solve for x

3. ## Re: Simultaneous Equations.

In case a graph helps...

g) $y=2x,y=2x^2$. The red line is $y=2x^2$ and the blue line is $y=2x$.

Clearly solutions are $x=0,1$

h) $y=6-x^2,y=4x+1$. The red line is $y=4x+1$ and the blue line is $y=6-x^2$.

Clearly solutions are $x=1,-5$

The value of y can be calculated just by substituting the value of x or by the graph.

4. ## Re: Simultaneous Equations.

Yet another way to do (g): $y=2x$ and $y=2x^2$:

If x and y are not 0, $\frac{y}{y}= /frac{2x^2}{2x}$, [tex]1= x[/itex]. And if x= 1, what is y?

That was "if x and y are not 0". It is easy to check that y is 0 if and only if x is and x= y= 0 satifies both equations.