Jose rents a bike for $4 plus $2.50 per hour. Elaine rents a
moped for $10 plus $1 per
hour. Write and solve the
system of equations to
determine at what point they
spend the same amount.

4 hours

Step-by-step explanation:

Let x be the # of hours spent using the vehicles

Jose: 4 + 2.5x

Elaine: 10 + x

If they spend the same amount then that means:

Elaine's price = Jose's price, therefore:

4 + 2.5x = 10 + x

1.5x = 6

x = 4

At 4 hours, both prices are the same.

They spend the same amount after 4 hours

answer: all the values are within because it has a pattern that repeats from -6 to 4.

good luck!

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = = -

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, - 8 ), then

- 8 = - + c ⇒ c = -

y = - x - ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form