Solve the system of linear equations by substitution.
{
x
+
y
=
8
x
−
y
=
4
(
6
,
2
)
(
5
,
1
)
(
6
,
3
)
(
4
,
2
)
The correct answer is (6,2).
To solve the system of linear equations by substitution, we can first solve one of the equations for one variable, and then substitute that expression into the other equation.
From the first equation, we can solve for x in terms of y:
x + y = 8
x = 8 - y
Now, we substitute this expression for x into the second equation:
8 - y - y = 4
8 - 2y = 4
-2y = -4
y = 2
Now that we have found the value of y, we can substitute it back into the expression we found for x:
x = 8 - 2
x = 6
Therefore, the solution to the system of linear equations is x = 6 and y = 2, which corresponds to the point (6,2).