b must be equal to -6 for infinitely many solutions for system of equations and
<u>Solution:
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Need to calculate value of b so that given system of equations have an infinite number of solutions
Let us bring the equations in same form for sake of simplicity in comparison
Now we have two equations
Let us first see what is requirement for system of equations have an infinite number of solutions
If and are two equation
then the given system of equation has no infinitely many solutions.
In our case,
As for infinitely many solutions
Hence b must be equal to -6 for infinitely many solutions for system of equations and
Answer:
nothing is seen
Step-by-step explanation:
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Find Slope :
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y = x/3 - 1
slope = 1/3
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Equation :
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y = mx + b
y = 1/3 x + b
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Find y-intercept :
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y = 1/3x + b
at point (4, 2),
2 = 1/3(4) + b
b = 2 - 4/3
b = 2/3
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Equation :
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y = 1/3x + 2/3
A / b = -2
Take note:
to have a quotient with at negative sign, both a & b must have opposites signs. a can be a positive number while b is a negative number or vice versa. If both a and b have the same sign, its quotient will be a positive number.
Let us disregard the sign.
To arrive at the answer of 2, a must be twice the amount of b. meaning a = 2b.
For example: look for a if b is equal to 2. a = 2(2) ; a = 4.
a / b = 2
4 / 2 = 2
2 = 2
Now, we consider the sign of both numbers. a can be 4 while b can be -2 OR vice versa.
a / b = -2
4 / -2 = -2 or -4 / 2 = -2