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Addition and Subtraction of Algebraic Expression

Subtract 3x-4...

Question

Subtract $3 x - 4 y - 7 z from the sum of x - 3 y + 2 z a n d - 4 x + 9 y = 11 z .$

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Solution

$sum of x - 3 y + 2 z a n d - 4 x + 9 y - 11 z = x - 3 y + 2 z + (- 4 x + 9 y - 11 z) = x - 3 y + 2 z - 4 x + 9 y - 11 z = x - 4 x - 3 y + 9 y + 2 z - 11 z = - 3 x + 6 y - 9 z N o w (- 3 x + 6 y - 9 z) - (3 x - 4 y - 7 z) = - 3 x + 6 y - 9 z - 3 x + 4 y + 7 z = - 3 x - 3 x + 6 y + 4 y - 9 z + 7 z = - 6 x + 10 y - 2 z$

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Similar questions

Q. Solve the following equations:

4 x - 3 y + 2 z = 40

5 x + 9 y - 7 z = 47

9 x + 8 y - 3 z = 97

3 x (x - 4 y + 5 z)

4 x (2 x - 3 y + 10 z)

Q. Show that each of the following systems of linear equations is consistent and also find their solutions:
(i) 6x + 4y = 2
9x + 6y = 3

(ii) 2x + 3y = 5
6x + 9y = 15

(iii) 5x + 3y + 7z = 4
3x + 26y + 2z = 9
7x + 2y + 10z = 5

(iv) x − y + z = 3
2x + y − z = 2
−x −2y + 2z = 1

(v) x + y + z = 6
x + 2y + 3z = 14
x + 4y + 7z = 30

(vi) 2x + 2y − 2z = 1
4x + 4y − z = 2
6x + 6y + 2z = 3

Q. State True or False:

8 x - 3 y + 7 z, - 4 x + 5 y - 4 z, - x - y - 2 z

3 x + y + z

.

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

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