Question

How many solutions does the system have? y=−2x+4

y=x^2−2x+4

Enter your answer in the box.

Answer 1

There is only one solution and the solution is (0,4).

Explanation:

The given system has equations;

`y=-2x+4`

and

`y=x^2-2x+4`

We equate the two equations to determine their point of intersection;

`x^2-2x+4=-2x+4`

`\Rightarrow x^2-2x+2x+4-4=0`

`\Rightarrow x^2=0`

`\Rightarrow x=0`

We put x=0 into the first equation to get;

`y=-2(0)+4=4`

There is only one solution and the solution is (0,4).