In the system of the equations 1-x-1-y-5-6- 1-y-1-z-7-12 and 1-z-1-x-3-4 the values of x- y and z are correctly denoted in which of the following options-

The correct option is A 3, 2 and 4Substituting 1/x, 1/y and 1/z as a, b, c, and then solving the given equations, we can get the values of x, y, z as 3, 2, 4 r ...

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Byju's Answer

Standard XII

Mathematics

Modulus Function

In the system...

Question

In the system of the equations $\frac{1}{x} + \frac{1}{y} = \frac{5}{6}, \frac{1}{y} + \frac{1}{z} = \frac{7}{12}$ and $\frac{1}{z} + \frac{1}{x} = \frac{3}{4}$ the values of x, y and z are correctly denoted in which of the following options?

4, 3 and 2

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3, 2 and 4

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2, 3 and 4

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3, 4 and 2

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None of these

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Solution

The correct option is B 3, 2 and 4
Substituting $\frac{1}{x}, \frac{1}{y} a n d \frac{1}{z}$ as $a, b, c$ , and then solving the given equations, we can get the values of $x, y, z$ as $3, 2, 4$ respectively.

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Similar questions

Q. In the system of equations

\frac{1}{x} + \frac{1}{y} = \frac{5}{6}, \frac{1}{y} + \frac{1}{z} = \frac{7}{12}

and

\frac{1}{z} + \frac{1}{x} = \frac{3}{4}

, values of x, y and z will be

Q. In the system of equation

\frac{1}{x} + \frac{1}{y} + \frac{1}{z} = 6, \frac{2}{x} - \frac{3}{y} + \frac{4}{z} = 8

and

\frac{3}{x} - \frac{4}{y} + \frac{5}{z} = 10

, values of

x

y

and

z

which satisfy the above three equations, will be

Q. (i) If

A = [\begin{matrix} 1 & - 2 & 0 \\ 2 & 1 & 3 \\ 0 & - 2 & 1 \end{matrix}]

, find A⁻¹. Using A⁻¹, solve the system of linear equations
x − 2y = 10, 2x + y + 3z = 8, −2y + z = 7

(ii)

A = [\begin{matrix} 3 & - 4 & 2 \\ 2 & 3 & 5 \\ 1 & 0 & 1 \end{matrix}]

, find A⁻¹ and hence solve the following system of equations:
3x − 4y + 2z = −1, 2x + 3y + 5z = 7, x + z = 2

(iii)

A = [\begin{matrix} 1 & - 2 & 0 \\ 2 & 1 & 3 \\ 0 & - 2 & 1 \end{matrix}] and B = [\begin{matrix} 7 & 2 & - 6 \\ - 2 & 1 & - 3 \\ - 4 & 2 & 5 \end{matrix}]

, find AB. Hence, solve the system of equations:
x − 2y = 10, 2x + y + 3z = 8 and −2y + z = 7

(iv) If

A = [\begin{matrix} 1 & 2 & 0 \\ - 2 & - 1 & - 2 \\ 0 & - 1 & 1 \end{matrix}]

, find A⁻¹. Using A⁻¹, solve the system of linear equations
x − 2y = 10, 2x − y − z = 8, −2y + z = 7

(v) Given

A = [\begin{matrix} 2 & 2 & - 4 \\ - 4 & 2 & - 4 \\ 2 & - 1 & 5 \end{matrix}], B = [\begin{matrix} 1 & - 1 & 0 \\ 2 & 3 & 4 \\ 0 & 1 & 2 \end{matrix}]

, find BA and use this to solve the system of equations
y + 2z = 7, x − y = 3, 2x + 3y + 4z = 17

(vi) If

A = (\begin{array}{rrr} 2 & 3 & 1 \\ 1 & 2 & 2 \\ - 3 & 1 & - 1 \end{array})

, find A^–1 and hence solve the system of equations 2x + y – 3z = 13, 3x + 2y + z = 4, x + 2y – z = 8.
(vii) Use product

[\begin{matrix} 1 & - 1 & 2 \\ 0 & 2 & - 3 \\ 3 & - 2 & 4 \end{matrix}] [\begin{matrix} - 2 & 0 & 1 \\ 9 & 2 & - 3 \\ 6 & 1 & - 2 \end{matrix}]

to solve the system of equations x + 3z = 9, −x + 2y − 2z = 4, 2x − 3y + 4z = −3.

Q. Solve the following system of equations by matrix method:
(i) x + y − z = 3
2x + 3y + z = 10
3x − y − 7z = 1

(ii) x + y + z = 3
2x − y + z = − 1
2x + y − 3z = − 9

(iii) 6x − 12y + 25z = 4
4x + 15y − 20z = 3
2x + 18y + 15z = 10

(iv) 3x + 4y + 7z = 14
2x − y + 3z = 4
x + 2y − 3z = 0

(v)

\frac{2}{x} - \frac{3}{y} + \frac{3}{z} = 10 \frac{1}{x} + \frac{1}{y} + \frac{1}{z} = 10 \frac{3}{x} - \frac{1}{y} + \frac{2}{z} = 13

(vi) 5x + 3y + z = 16
2x + y + 3z = 19
x + 2y + 4z = 25

(vii) 3x + 4y + 2z = 8
2y − 3z = 3
x − 2y + 6z = −2

(viii) 2x + y + z = 2
x + 3y − z = 5
3x + y − 2z = 6

(ix) 2x + 6y = 2
3x − z = −8
2x − y + z = −3

(x) x − y + z = 2
2x − y = 0
2y − z = 1

(xi) 8x + 4y + 3z = 18
2x + y +z = 5
x + 2y + z = 5

(xii) x + y + z = 6
x + 2z = 7
3x + y + z = 12

(xiii)

\frac{2}{x} + \frac{3}{y} + \frac{10}{z} = 4, \frac{4}{x} - \frac{6}{y} + \frac{5}{z} = 1, \frac{6}{x} + \frac{9}{y} - \frac{20}{z} = 2; x, y, z \neq 0

(xiv) x − y + 2z = 7
3x + 4y − 5z = −5
2x − y + 3z = 12

Which of the following options holds true for the system of equations,

x + y + z =6

x + 2y + 3z = 12

x + 4y + 7z =30

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In the system of the equations 1x+1y=56,1y+1z=712 and 1z+1x=34 the values of x, y and z are correctly denoted in which of the following options?

The correct option is B 3, 2 and 4Substituting 1x,1y and 1z as a,b,c, and then solving the given equations, we can get the values of x,y,z as 3,2,4 respectively.

In the system of the equations $\frac{1}{x} + \frac{1}{y} = \frac{5}{6}, \frac{1}{y} + \frac{1}{z} = \frac{7}{12}$ and $\frac{1}{z} + \frac{1}{x} = \frac{3}{4}$ the values of x, y and z are correctly denoted in which of the following options?

The correct option is B 3, 2 and 4
Substituting $\frac{1}{x}, \frac{1}{y} a n d \frac{1}{z}$ as $a, b, c$ , and then solving the given equations, we can get the values of $x, y, z$ as $3, 2, 4$ respectively.