Which of the following equations have x -4 and y -2 as a solution-A- 2 x-3 y-12B- 4 x - y -19C- x-y-6D- 3 x-2 y-15

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Linear Equation in 2 Variables

Which of the ...

Question

Which of the following equations have $x = 4 and y = 2$ as a solution?

$2 x + 3 y = 12$

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$4 x + y = 19$

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$x + y = 6$

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$3 x + 2 y = 15$

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Solution

The correct option is C
$x + y = 6$

Putting $x = 4$ and $y = 2$ in each of the given equations, we get the following:

$2 x + 3 y = 12$ :
LHS $= 2 \times 4 + 3 \times 2 = 14 \neq$ RHS

$4 x + y = 19$ :
LHS $= 4 \times 4 + 2 = 18 \neq$ RHS

$x + y = 6$ :
LHS $= 4 + 2 = 6 =$ RHS

$3 x + 2 y = 15$ :
LHS $= 3 \times 4 + 2 \times 2 = 16 \neq$ RHS

Hence, $x = 4, y = 2$ is a solution of the equation $x + y = 6$ .

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Q. Which of the following pairs of linear equations are consistent/inconsistent? If consistent, obtain the solution graphically:

(i)

x + y = 5, 2 x + 2 y = 10

(ii)

x - y = 8, 3 x - 3 y = 16

(iii)

2 x + y - 6 = 0, 4 x - 2 y - 4 = 0

(iv)

2 x - 2 y - 2 = 0, 4 x - 4 y - 5 = 0

Which of the following pairs of linear equations is inconsistent?
$1. x + 3 y - 5 = 0, 2 x + y = 0$
$2. 2 x + y = 1, 2 y = 2 - 4 x$
$3. 2 x - y = 2, 2 y - 4 x = 2$

Q. Solve the following simultaneous equations graphically.
(1) 2x + 3y = 12 ; x – y = 1
(2) x – 3y = 1 ; 3x – 2y + 4 = 0
(3) 5x – 6y + 30 = 0 ; 5x + 4y – 20 = 0
(4) 3x – y – 2 = 0 ; 2x + y = 8
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Which of the following equations have x=4 and y=2 as a solution?

The correct option is C x+y=6 Putting x=4 and y=2 in each of the given equations, we get the following: 2x+3y=12: LHS =2×4+3×2=14≠ RHS 4x+y=19: LHS =4×4+2=18≠ RHS x+y=6: LHS =4+2=6= RHS 3x+2y=15: LHS =3×4+2×2=16≠ RHS Hence, x=4,y=2 is a solution of the equation x+y=6.

Which of the following equations have $x = 4 and y = 2$ as a solution?