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Standard IX

Mathematics

Solving Equations Using Method of Elimination

Solve x + 4y ...

Question

Solve x + 4y = 14 & 7x - 3y = 5

x = 1, y = 4

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x = 2, y = 3

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x = 9, y = 7

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x = 0, y = 4

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Solution

The correct option is B $x = 2, y = 3$
$x + 4 y = 14$
$x = 14 - 4 y$ .........(i)
$7 x - 3 y = 5$ .........(ii)
Substituting the value of x in equation (ii)
⇒ $7 (14 - 4 y) - 3 y = 5$
⇒ $98 - 28 y - 3 y = 5$
⇒ $98 - 31 y = 5$
⇒ $93 = 31 y$
⇒ $y = \frac{93}{31} \Rightarrow y = 3$
Now substituting value of y in equation (ii)
⇒ $7 x - 3 (3) = 5$
⇒ $7 x - 3 (3) = 5$
⇒ $7 x = 14$
⇒ $x = \frac{14}{7} = 2$
So solution is x = 2 and y = 3

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Similar questions

Q. Solve the following simultaneous equations graphically.
(1) x + y = 6 ; x – y = 4
(2) x + y = 5 ; x – y = 3
(3) x + y = 0 ; 2x – y = 9
(4) 3x – y = 2 ; 2x – y = 3
(5) 3x – 4y = –7 ; 5x – 2y = 0
(6) 2x – 3y = 4 ; 3y – x = 4

Q. Solve the following systems of linear inequations graphically:

(i) 2x + 3y ≤ 6, 3x + 2y ≤ 6, x ≥ 0, y ≥ 0
(ii) 2x + 3y ≤ 6, x + 4y ≤ 4, x ≥ 0, y ≥ 0
(iii) x − y ≤ 1, x + 2y ≤ 8, 2x + y ≥ 2, x ≥ 0, y ≥ 0
(iv) x + y ≥ 1, 7x + 9y ≤ 63, x ≤ 6, y ≤ 5, x ≥ 0, y ≥ 0
(v) 2x + 3y ≤ 35, y ≥ 3, x ≥ 2, x ≥ 0, y ≥ 0

Q. Solve the following pairs of equations by reducing them to a pair of linear equations:

(i)

\frac{1}{2 x} + \frac{1}{3 y} = 2; \frac{1}{3 x} + \frac{1}{2 y} = \frac{13}{6}

(ii)

\frac{2}{\sqrt{x}} + \frac{3}{\sqrt{y}} = 2; \frac{4}{\sqrt{x}} - \frac{9}{\sqrt{y}} = - 1

(iii)

\frac{4}{x} + 3 y = 14; \frac{3}{x} - 4 y = 23

(iv)

\frac{5}{x - 1} + \frac{1}{y - 2} = 2; \frac{6}{x - 1} - \frac{3}{y - 2} = 1

(v)

\frac{7 x - 2 y}{x y} = 5; \frac{8 x + 7 y}{x y} = 15

(vi)

6 x + 3 y = 6 x y; 2 x + 4 y = 5 x y

(vii)

\frac{10}{x + y} + \frac{2}{x - y} = 4; \frac{15}{x + y} - \frac{5}{x - y} = - 2

(viii)

\frac{1}{3 x + y} + \frac{1}{3 x - y} = \frac{3}{4}; \frac{1}{2 (3 x + y)} - \frac{1}{2 (3 x - y)} = \frac{- 1}{8}

Q. Solve the following simultaneous equations.
(1)

\frac{2}{x} + \frac{2}{3 y} = \frac{1}{6}; \frac{3}{x} + \frac{2}{y} = 0

(2)

\frac{7}{2 x + 1} + \frac{13}{y + 2} = 27; \frac{13}{2 x + 1} + \frac{7}{y + 2} = 33

(3)

\frac{148}{x} + \frac{231}{y} = \frac{527}{x y}; \frac{231}{x} + \frac{148}{y} = \frac{610}{x y}

(4)

\frac{7 x - 2 y}{x y} = 5; \frac{8 x + 7 y}{x y} = 15

(5)

\frac{1}{2 (3 x + 4 y)} + \frac{1}{5 (2 x - 3 y)} = \frac{1}{4}; \frac{5}{(3 x + 4 y)} - \frac{2}{(2 x - 3 y)} = - \frac{3}{2}

Solve the following systems of linear inequations graphically :

$(i) 2 x + 3 y \leq 6, 3 x + 2 y \leq 6, x \geq 0, y \geq 0 (i i) 2 x + 3 y \leq 6, x + 4 y \leq 4, x \geq 0, y \geq 0 (i i i) x + y \geq 1, x + 2 y \leq 8, 2 x + y \geq 2, x \geq 0, y \geq 0 (i v) x + y \geq 1, 7 x + 9 y \leq 63, y \leq 5, x \geq 0, y \geq 0 (v) 2 x + 3 y \leq 35, y \geq 3, x \geq 2, x \geq 0, y \geq 0$

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