2x + 6y = −6, 4x − 3y = −12

What is the solution to the system of equations?

(
,
)

x=-3, y=0. (-3, 0).

Step-by-step explanation:

2x+6y=-6

4x-3y=-12

-2(2x+6y)=-2(-6)

4x-3y=-12

-4x-12y=12

4x-3y=-12

-15y=0

y=0/-15=0

2x+6(0)=-6

2x=-6

x=-6/2

x=-3

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240