Answer:
The value of b is 9.5
Step-by-step explanation:
If a system of equations has infinitely many solutions, that means the two equations are equal
If the system of equations ax + by = c, dx + ey = f, then
- a = d ⇒ coefficients of x
- b = e ⇒ coefficients of y
Let us use this fact to solve the question
∵ 3x - y = 19 ⇒ (1)
∵ 1.5x - 0.5 y = b ⇒ (2)
∵ This system of equations has infinitely many solutions
∴ The coefficients of x must be equal
∴ The coefficients of y must be equal
∴ The numerical terms must be equal
→ Multiply equation (2) by 2 to make the coefficients of x and y on it
equal the coefficients of x and y in equation (1)
∵ 2(1.5x) - 2(0.5y) = 2(b)
∴ 3x - y = 2b ⇒ (3)
→ By comparing equations (1) and (3), 19 must equal 2b
∵ 2b = 19
→ Divide both sides by 2
∴ b = 9.5
∴ The value of b is 9.5
