Question

Paige is comparing costs for renting a steam cleaner from two different stores. Each store charges a set rental fee plus an hourly rate for each hour the steam cleaner is rented.

The costs for each store are represented in this system of equations where x is the hours rented and y is the total cost for renting the machine.



{
15
x
+
45
=
y
20
x
+
35
=
y



Which matrix equation is equivalent to the system of equations above?


[
15
45
20
35
]
[
x
y
]
=
[
1
1
]


[
15
−
1
20
−
1
]
[
x
y
]
=
[
−
45
−
35
]


[
15
−
1
20
−
1
]
[
x
y
]
=
[
45
35
]


[
15
45
20
35
]
[
x
y
]
=
[
−
1
−
1
]

Answer 1

Rewrite each equation as 15x - y = -45 and 20x - y = -35. That gives the matrix form

[15 -1
20 -1] [x
y] = [-45
-35].

So the correct choice is the second one.