Solve the systems : 1) x = 3y 3x + y = 10 2) 2x + 7y = 1 2x - 2y = 9

We'll solve the first system of equations using
substitution
technique:

x=3y

We'll
substitute x by 3y, in the second equation of the
system:

3*3y+y=10

We'll
combine like
terms:

9y+y=10

10y=10

We'll
divide by 10 both
sides:

y=1

Now,
all we'll substitute the value for y into the first
equation:

x=3y

x=3*1

x=3

The
solution of the system is {(1 , 3)}.

Let's
solve the second system of equations:

2x + 7y =
1

2x - 2y = 9

We'll solve this
system using the substitution
method:

2x=1-7y

Now, instead
of 2x, we'll write in the second equation 1-7y.

1 - 7y - 2y
=9

We'll combine like terms:

1
- 9y=9

We'll subtract 1 both
sides:

-9y=8

We'll divide by
-9 both
sides:

y=-8/9

But 2x=1-7y
and y=-8/9.

2x = 1 + 7*8/9

2x
= 1 + 56/9

2x = (9+56)/9

2x =
65/9

We'll divide by
2:

x =
65/18

The solution of the
system is: {(-8/9 , 65/18)}.