Answer to Question #344643 in Algebra for dodo

Question #344643

Solve this system of equations and provide a graphical representation of the solution. (12)


x2 + y2 = 5


x + y = 1


1
Expert's answer
2022-05-30T23:09:18-0400

We can solve this system by substitution.

From the second equation we have:


"y=1-x."


Then we can rewrite the first equation and solve it:

"x^2+(1-x)^2=5,"

"x^2+1-2x+x^2=5,"  (we opened parentheses)

"2x^2-2x-4=0,"  (we added the similar terms)

"x^2-x-2=0,"  (we divided the equation by 2)

"x^2-2x+x-2=0,"

"x(x-2)+1(x-2)=0,"

(x-2)(x+1)=0,

"x-2=0"  or "x+1=0,"

"x_1=2""x_2=-1."

Now we can find the y:

"y_1=1-x_1=1-2=-1,"

"y_2=1-x_2=1-(-1)=2."

So, we have two points:  (2,-1) and (-1,2).

The graphical representation.

The graphical representation of the first equation is circle with the center in (0;0) and radius , the graphical representation of the second equation is straight line "y=1-x" .



The graphical representation of solution are points of intersection: (2,-1) and (-1,2).


Answer: (2,-1) and (-1,2).


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