chloe081
02.12.2020 •
Mathematics
In the system of equations, b is a constant. If the system has infinitely many solutions, what is the value of b?
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Ответ:
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 xb = e ⇒ coefficients of yc = f ⇒ numerical termsLet 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
Ответ:
142048
Step-by-step explanation: