Solve the system of linear equations by substitution.
{
y
=
3
x
+
1
2
x
+
y
=
16
(
3
,
10
)
(
3
,
7
)
(
2
,
10
)
(
5
,
9
)
To solve the system of equations by substitution, we need to substitute the value of y from the first equation into the second equation.
From the first equation, we have y = 3x + 1. Now substitute this into the second equation:
2x + (3x + 1) = 16
2x + 3x + 1 = 16
5x + 1 = 16
5x = 15
x = 3
Now that we have found the value of x, we can substitute it back into the first equation to find the value of y:
y = 3(3) + 1
y = 9 + 1
y = 10
Therefore, the solution to the system of equations is (3, 10).