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Expression Formation

Subtract 2x...

Question

Subtract $(2 x - 4 y + 3 z)$ from the sum of $(x + 3 y - 4 z), (2 x + y - z)$ and $(- 2 x + 3 y - z)$ .

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Solution

$(x + 3 y - 4 z) + (2 x + y - z) + (- 2 x + 3 y - z) - (2 x - 4 y + 3 z)$
$= (x + 2 x + 3 y + y - 4 z - z) + (- 2 x + 3 y - z) - (2 z - 4 y + 3 z)$
$= (3 x + 4 y - 5 z) + (- 2 x + 3 y - z) - (2 x - 4 y + 3 z)$
$= (x + 7 y - 6 z) - (2 x - 4 y + 3 z)$
$= x - 2 x + 7 y + 4 y - 6 z - 3 z$
$= - x + 11 y - 9 z$
$∴$ Ans is $(- x + 11 y - 9 z)$

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Similar questions

Q. Subtract the sum of 13x − 4y + 7z and −6z + 6x + 3y from the sum of 6x − 4y − 4z and 2x + 4y − 7.

2 x - 3 y + 4 z

4 x - 6 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

Q. The value of

x, y

z

respectively on simplifying the equation

2 x + 3 y = 0

3 y + 4 z = 14

2 x + 4 z = 26

Q. The value of

x, y

z

respectively, on simplifying the equations

2 x + 3 y = 0, 3 y + 4 z = 14, 2 x + 4 z = 26

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