y=-3x +19
y=2x=1
need to know whether the equation are independent,dependent or inconsistent
To determine whether the given equations are independent, dependent, or inconsistent, we need to compare the slopes of the two lines.
Let's first rewrite the equations in the standard form: y = mx + b, where m represents the slope and b represents the y-intercept.
Equation 1: y = -3x + 19
Comparing it with the standard form, we can see that the slope (m1) of this equation is -3.
Equation 2: y = 2x + 1
Comparing it with the standard form, we can see that the slope (m2) of this equation is 2.
Now, let's analyze the possibilities:
1. Independent: If the slopes of the two lines are different, the equations are independent. In this case, m1 ≠ m2.
2. Dependent: If the slopes of the two lines are the same and the y-intercepts are also the same, the equations are dependent. In this case, m1 = m2 and b1 = b2.
3. Inconsistent: If the slopes of the two lines are the same, but the y-intercepts are different, the equations are inconsistent. In this case, m1 = m2, but b1 ≠ b2.
Now, let's compare the slopes:
m1 = -3 and m2 = 2
Since the slopes of the two lines are different (m1 ≠ m2), the given equations are independent.