Step-by-step explanation:
a.
simply add both equations
x + y = 2
-3x - y = 5
----------------
-2x + 0 = 7
x = -7/2
x + y = 2
-7/2 + y = 2
y = 2 + 7/2 = 4/2 + 7/2 = 11/2
b.
1/2 x + 2y = -13
x - 4y = 8
first multiply the first equating by 2
x + 4y = -26
x - 4y = 8
--------------------
2x + 0 = -18
x = -18/2 = -9
x - 4y = 8
-9 - 4y = 8
-4y = 17
y = -17/4
The Number of boys in the class is: 18
Let's call "g" to the number of girls in the class.
The problem says that there is "w" fewer boys than girls, so we have:
g-w=18
Then, the number of girls in the class is:
g=18+w
Let's call "x" to the total number of studens in the class:
x=g+18
When we substitute g=18+w into x=g+18, we obtain:
x= (18+w)+18
The total number of studens in the class is:
x=w+36
So you want to make it: total distance (d) = rate (r) × total time (t), solving for r: r = d / t
r = (420mi) / (3h+214h), r = 420mi / 217h
r = 1.935mi/h = 1.94mi/h