Question

The points (2a, – 4a + 3), (2b - 3, b) lie on the graph of the equation

Answer 1

Answer:

• a = -2.5, b = 1

Step-by-step explanation:

Given line:

• y = -3x - 2

Points on the same line:

• (2a, -4a + 3) and (2b - 3, b)

Substitute x and y values of both points into equation of the line and solve for a and b:

• -4a + 3 = -3(2a) - 2 ⇒ -4a + 3 = -6a - 2 ⇒ 6a - 4a = -2 - 3 ⇒ 2a = -5 ⇒ a = -2.5
• b = -3(2b - 3) - 2 ⇒ b = -6b + 9 - 2 ⇒ b+ 6b = 7 ⇒ 7b = 7 ⇒ b = 1

Answer 2

Answer:

The points (2a, – 4a + 3), (2b - 3, b) lie on the graph of the equation y = -3x - 2

Now,

By substituting x and y with the value of the points, we get

$- 4a + 3 = - 3(2a) - 2 \\ - 4a + 3 = - 6a - 2 \\ 6a - 4a = - 3 - 2 \\ 2a = - 5 \\ a = \frac{( - 5)}{2} \\ \boxed{a = - 2.5}$

$\\ b =- 3(2b - 3) - 2 \\ b = - 6b + 9 - 2 \\ b + 6b = 9 - 2 \\ 7b = 7 \\ b = \frac{7}{7} \\ \boxed{b = 1}$

Therefore,

• The value of a is -2.5.
• The value of b is 1.