Solve the following system of equations using the substitution method

5x+3y=1
X+2y=3

  (x, y) = (-1, 2)

Step-by-step explanation:

Substitution is easier if you already have an expression for the variable you want to make a substitution for. Here, we don't have that, but we have an equation with x having a coefficient of 1. We can use that to write an expression for x:

  x = 3 -2y . . . . . subtract 2y from both sides of the second equation

  5(3 -2y) +3y = 1 . . . . substitute for x in the first equation

  15 -10y +3y = 1 . . . . . eliminate parentheses

  -7y = -14 . . . . . . . . . . subtract 15, collect terms

  y = 2 . . . . . . . . . . . . . divide by -7

Use this value in the equation for x:

  x = 3 -2(2)  = -1

The solution is (x, y) = (-1, 2).

astronomers is your final answer! : )

(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