Please help me and do by substitution. Please show work

Mathematics

1 answer:

Stels [109]3 years ago

4 0

$\left\{\begin{array}{ccc}x^2+y-8=0\\x+y-2=0&|+2\end{array}\right\\\left\{\begin{array}{ccc}x^2+y-8=0\\x+y=2&|-x\end{array}\right\\\left\{\begin{array}{ccc}x^2+y-8=0\\y=2-x\end{array}\right\\\\\text{subtitute y=2-x to the first equation}\\\\x^2+2-x-8=0\\\\x^2-x-6=0\\\\x^2+2x-3x-6=0\\\\x(x+2)-3(x+2)=0\\\\(x+2)(x-3)=0\iff x+2=0\ \vee\ x-3=0\\\\x=-2\ \vee\ x=3\\\\\text{for}\ x=-2\to y=2-(-2)=2+2=4\\\text{for}\ x=3\to y=2-3=-1\\\\Answer:\ x=-2,\ y=4\to(-2,\ 4)\ and\ x=3,\ y=-1\to(3,\ -1)$

You might be interested in

In 2005, the shabelle river in Somalia rose an estimated 5.25 inches every hour for 15 hours. The increase in water level is rep

Georgia [21]

Answer:

The Given situation is In 2005, the shabelle river in Somalia rose an estimated 5.25 inches every hour for 15 hours.

Increase in water level is represented by the function,f(x)=5.25 x.

or replacing f(x) by y we get ,y= 5.25 x

This is equation of straight line passing through the origin.

As x is number of hours , so x> 0,(0,∞] Which is it's domain.

As x> 0, so Range is those values of y for which x is defined.

$x= \frac{y}{5.25}$ ,So Range is y>0 i.e (0,∞}

As the function has no breaking point , that is when you plot the graph on coordinate axis there is no breaking point.So , it is everywhere continuous i. e for all values of x.