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Solving Equations Algebraically

Add:5 x-8 y+2...

Question

Add:
5x − 8y + 2z, 3z − 4y − 2x, 6y − z − x and 3x − 2z − 3y

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Solution

Writing the terms of the given expressions (in the same order) in the form of rows with like terms below each other and adding column-wise, we get:

$5 x - 8 y + 2 z - 2 x - 4 y + 3 z - x + 6 y - z 3 x - 3 y - 2 z 5 x - 9 y + 2 z$

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Similar questions

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

5 x - 4 y - {7 x - (3 z - 2 y) + 4 z - 3 (x + 3 y - 2 z)}] =

Q. Simplify:
5x − [4y − {7x − (3z − 2y) + 4z − 3(x + 3y − 2z)}]

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

∣ ∣ ∣ ∣ \begin{matrix} x & x + y & x + y + z 2 x & 3 x + 2 y & 4 x + 3 y + 2 z 3 x & 6 x + 3 y & 10 x + 6 y + 3 z \end{matrix} ∣ ∣ ∣ ∣

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