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).

for this case we must apply distributive property to the following expression:

the distributive property states that:

then, when applying the property we have to multiply the -2 for each term within the parenthesis:

this is a direct variation proportion. y = kx

y is the total amount due, k is the constant of variation, and x is the number of texts sent.

plug in the 3.20 and the 16 to solve for the "k". this is the constant of proportionality. it is the value that will not change.

3.20 = k(16). solving you get $.20 per text.

the equation would then be y = .20x