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. In matrix form:

[ [15, −1],
[20, −1] ] [x, y]^T = [−45, −35]^T

So the correct choice is the second option.