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Graphical Method of Finding Solution of a Pair of Linear Equations

Solve the fol...

Question

Solve the following linear equations :
(i) x – 11 =7
(ii) z + 8 = 9
(iii) 11x = 121

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Solution

(i) x – 11 = 7
x = 7 + 11
x = 18

(ii) z + 8 = 9
z = 9 -8
z =1

(iii) 11x = 121
x = $\frac{121}{11}$
x = 11

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Q. Solve the following simultaneous linear equations by method of reduction.

x + 2 y + z = 8

2 x + 3 y - z = 11

3 x - y - 2 z = 5

Q. Solve the following equations:

12 x + 8 y - 11 z = - 3

11 x - 13 y - z = 2

8 x + 17 y - 12 z = - 2

I) -7

ii) 9

iii) -6

iv) 0

v) 1

Q. Solve the following system of linear equations in three variables.
2x - 7y + 11z = 0
6x - 8y + 7z = 0
3x + 4y + 5z = 35

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

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Graphical Method of Finding Solution of a Pair of Linear Equations

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