If the system of linear equations $ 8 x+y+4 z=-2 $, $ x+y+z=0 $, $ \lambda x-3 y=\mu$ has infinitely many solutions, then the distance of the point $\left(\lambda, \mu,-\frac{1}{2}\right)$ from the plane $8 x + y +4 z +2=0$ is :
- $3 \sqrt{5}$
- 4
- $\frac{26}{9}$
- $\frac{10}{3}$
The Correct Option is D
Solution and Explanation
The correct option is (D): $\frac{10}{3}$
Top Questions on linear inequalities in one variable
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Concepts Used:
Linear Inequalities in One Variable
The graph of a linear inequality in one variable is a number line. We can use an open circle for < and > and a closed circle for ≤ and ≥.
Inequalities that have the same solution are commonly known as equivalents. There are several properties of inequalities as well as the properties of equality. All the properties below are also true for inequalities including ≥ and ≤.
The addition property of inequality says that adding the same number to each side of the inequality gives an equivalent inequality.
If x>y, then x+z>y+z If x>y, then x+z>y+z
If x<y, then x+z<y+z If x<y, then x+z<y+z
The subtraction property of inequality tells us that subtracting the same number from both sides of an inequality produces an equivalent inequality.
If x>y, then x−z>y−z If x>y, then x−z>y−z
If x<y, then x−z<y−z Ifx<y, then x−z<y−z
The multiplication property of inequality tells us that multiplication on both sides of an inequality with a positive number gives an equivalent inequality.
If x>y and z>0, then xz>yz If x>y and z>0, then xz>yz
If x<y and z>0, then xz<yz If x<y and z>0,then xz<yz