Solve the following system of equations
x^2+2y^2=59
2x^2+y^2=43

x = (-3,3), y = (-5,5)

Step-by-step explanation:

Add both of the equations together, for . Now we can divide both sides by 3, getting. we subtract the first equation from our equation we just got, getting y= (5,-5). once we plug that in, we get , x = (-3,3)

both graphs increase on their domain

neither graph has a y-intercept

step-by-step explanation:

the following points can be visualized easily from the graph

center (1,3) with radius 6

step-by-step explanation:

we must complete the square to find the center and radius of the circle.

first make sure the x and y squared terms have 1 as their coefficients. we also make sure x and y terms together.

we now create space between the x and y terms with parenthesis.

we complete the square by taking the middle terms -2x and the -6y - divide each and square them.

we add the squares to both sides.

simplify.

and write the quadratics in factored form.

the center is (h,k) or (1,3). the radius is the square root of 36 which is 6.