Answer:
Both of them are correct.
Explanation:
Both of them are correct.
EQ. 1) y = -2x + 3
EQ. 2) 6x + 3y = 9
Transform EQ. 2 into its slope-intercept form, y = mx + b:
6x + 3y = 9
6x - 6x + 3y = -6x + 9
3y = -6x + 9
3y/3 = (-6x + 9)/3
y = -2x + 3 (As you can see, Equation 2 is equivalent to Equation 1's).
Given that Equations 1 and 2 are equivalent, their lines will coincide on top of each other (as if they're the same line) once graphed.
Therefore, the systems of linear equations will have infinitely many solutions.
Let's see why Charles and Destiny are both correct with their claims.
If you plug in Charles' coordinates (3, -3) in both equations,
EQ. 1) y = -2x + 3
-3 = -2(3) + 3
-3 = -6 + 3
-3 = -3 (True statement)
EQ. 2) 6x + 3y = 9
6(3) + 3(-3) = 9
18 - 9 = 9
9 = 9 (True statement)
Do the same thing for Destiny's coordinates: (-1, 5)
EQ. 1) y = -2x + 3
5 = -2(-1) + 3
5 = 2 + 3
5 = 5 (True statement)
EQ. 2) 6x + 3y = 9
6(-1) + 3(5) = 9
-6 + 15 = 9
9 = 9 (True statement)
With these calculations, it shows that both of their coordinates are solutions to the given systems of linear equations.