Answer:
The only point that satisfies both equations simultaneously is (3, 0).
Explanation:
To determine which point is a solution to the given system of linear equations, we need to substitute the coordinates of each point into the equations and see which point(s) satisfy both equations simultaneously.
Given system of linear equations:
y = −x + 3
x − 3y = 3
Substituting the coordinates of each point, we get:
(0, 3):
y = −x + 3 => 3 = -0 + 3 => 3 = 3 (satisfied)
x − 3y = 3 => 0 - 9 = 3 => -9 ≠ 3 (not satisfied)
(1, 2):
y = −x + 3 => 2 = -1 + 3 => 2 = 2 (satisfied)
x − 3y = 3 => 1 - 6 = 3 => -5 ≠ 3 (not satisfied)
(3, 0):
y = −x + 3 => 0 = -3 + 3 => 0 = 0 (satisfied)
x − 3y = 3 => 3 - 0 = 3 => 3 = 3 (satisfied)
(4, −1):
y = −x + 3 => -1 = -4 + 3 => -1 = -1 (satisfied)
x − 3y = 3 => 4 - (-3) = 3 => 7 ≠ 3 (not satisfied)
Therefore, the only point that satisfies both equations simultaneously is (3, 0).