Find the value of x and y:
$5 x - 3 y = 11$ , $10 x + 6 y = - 22$

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Solution

Let the equation
$5 x - 3 y = 11$ ----- (i)
$10 x + 6 y = - 22$ ----- (ii)

From (i)
$y = \frac{5 x - 11}{3}$

put the value of $y$ in (ii)
$10 x + 6 (\frac{5 x - 11}{3}) = - 22$

$30 x + 30 x - 66 = - 66$

$x = 0$

put $x = 0$ in (i), we get

$0 - 3 y = 11$

$y = - \frac{11}{3}$

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Similar questions

Q. On comparing the ratios

\frac{a_{1}}{a_{2}}, \frac{b_{1}}{b_{2}}

and

\frac{c_{1}}{c_{2}}

, find out whether the following pairs of linear equations are consistent, or inconsistent.

5 x - 3 y = 11; - 10 x + 6 y = 22

Question 3 (iv)
On comparing the ratios $\frac{a_{1}}{a_{2}}$ , $\frac{b_{1}}{b_{2}}$ and $\frac{c_{1}}{c_{2}}$ find out whether the following pair of linear equations are consistent, or inconsistent.
5x - 3y= 11 ; -10x+ 6y= -22

Q. Using substitution method find the value of x and y:

2 x - 3 y = 2

and

5 x - 6 y = 2

Q. On comparing the ratios

\frac{a_{1}}{a_{2}}, \frac{b_{1}}{b_{2}}

and

\frac{c_{1}}{c_{2}}

, find out whether the following pair of linear equations are consistent, or inconsistent.
(i)

3 x + 2 y = 5; 2 x - 3 y = 7

(ii)

2 x - 3 y = 8; 4 x - 6 y = 9

(iii)

\frac{3}{2} x + \frac{5}{3} y = 7; 9 x - 10 y = 14

(iv)

5 x - 3 y = 11; - 10 x + 6 y = - 22

(v)

\frac{4}{3} x + 2 y = 8; 2 x + 3 y = 12

Q. Solve for

x

and

y

5 x + 6 y = 7 x + 3 y = 3 (x + 6 y - 6)

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Find the value of x and y:5x−3y=11, 10x+6y=−22

Let the equation 5x−3y=11 ----- (i)10x+6y=−22 ----- (ii)From (i)y=5x−113put the value of y in (ii)10x+6(5x−113)=−2230x+30x−66=−66x=0put x=0 in (i), we get0−3y=11y=−113

Find the value of x and y:
$5 x - 3 y = 11$ , $10 x + 6 y = - 22$

Let the equation
$5 x - 3 y = 11$ ----- (i)
$10 x + 6 y = - 22$ ----- (ii)

From (i)
$y = \frac{5 x - 11}{3}$

put the value of $y$ in (ii)
$10 x + 6 (\frac{5 x - 11}{3}) = - 22$

$30 x + 30 x - 66 = - 66$

$x = 0$

put $x = 0$ in (i), we get

$0 - 3 y = 11$

$y = - \frac{11}{3}$