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Addition and Subtraction of Algebraic Expression

State True or...

Question

State True or False:
Addition of $8 x - 3 y + 7 z, - 4 x + 5 y - 4 z, - x - y - 2 z$ is $3 x + y + z$ .

A

True

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B

False

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Solution

The correct option is A True
$W e c a n d i r e c t l y a d d t h e c o e f f i c i e n t s o f l i k e v a r i a b l e s, ⟹ (8 - 4 - 1) x + (- 3 + 5 - 1) y + (7 - 4 - 2) z = 3 x + y + z$

Hence the given statement is true.

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Similar questions

Q. State whether True or False.

(3 y + 4 z) (3 y - 4 z) + (2 y + 7 z) (y + z)

11 y^{2} + 9 y z - 9 z^{2}

.

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

Q. Show that each one of the following systems of linear equation is inconsistent:
(i) 2x + 5y = 7
6x + 15y = 13

(ii) 2x + 3y = 5
6x + 9y = 10

(iii) 4x − 2y = 3
6x − 3y = 5

(iv) 4x − 5y − 2z = 2
5x − 4y + 2z = −2
2x + 2y + 8z = −1

(v) 3x − y − 2z = 2
2y − z = −1
3x − 5y = 3

(vi) x + y − 2z = 5
x − 2y + z = −2
−2x + y + z = 4

Q. The system of equations

x + y - 2 z = 0

2 x - 3 y + z = 0

x - 5 y + 4 z = k

is consistent for

Q. Solve the following systems of equations.

2 x + 3 y - z = 6, x - y + 7 z = 8, 3 x - y + 2 z = 7

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