Question

Substitution, Cross Multiplication
a)x -y =3, 2x+5y=12
b) 3x - 4y - 1=0, 2x -y-5=0​

Answer 1

HOLA !!!

ANSWER :-

a) $x = 27 \div 7$

$y = 6 \div 7$

b) $x = 19\div 5$

$y = 13 \div 5$

EXPLAINATION :-

IT IS IN THE ATTACHED PHOTOS.

HOPE IT HELPS UHH #CHEERS

Answer 2

SOLUTION

{SUBSTITUTION}

a). x-y=3

2x+5y=12

=) x-y=3-------(1)

=) 2x+5y=12-----(2)

From (1)

=)x-y= 3

=) x= 3+y

Putting value of x in (2)

=)2(3+y)+5y=12

=) 6+2y+5y=12

=)6+7y= 12

=)7y= 12-6

=)7y=6

=)y= 6/7

Putting y = 6/7 in (1)

=)x-y= 3

=) x- 6/7=3

=) x= 3+6/7

=) x= 21+6/7

=)x= 27/7

{CROSS MULTIPLICATION}

x-y-3=0

2x+5y-12=0

$= > \frac{1}{2} \: \times \: \frac{ - 1}{5} \: \times \frac{ - 3}{ - 12} \: \times \frac{1}{2} \\ \\ = > \frac{x}{( - 1) \times( - 12) - 5 \times ( - 3) } = \frac{y}{( - 3) \times 2 - ( - 12) \times 1} = \frac{1}{1 \times 5 - 2 \times ( -1)} \\ \\ = > \frac{x}{12 + 15} = \frac{y}{( - 6) + 12} = \frac{1}{5 + 2} \\ = > \frac{x}{27} = \frac{y}{6} = \frac{1}{7} \\ \\ = > now \\ = > \frac{x}{27} = \frac{1}{7} \: \: or \: \: \frac{y}{6} = \frac{1}{7} \\ \\ = > 7x = 27 \: \: or \: \: 7y = 6 \\ \\ = > x = \frac{27}{7} \: \: \: or \: \: \: y = \frac{6}{7} answer$

2).3x-4y-1=0

2x-y-5=0

{SUBSTITUTION}

=)3x=1+4y--------(1)

=)2x= y+5---------(2)

From(1)

=)x= 1+4y/3

Putting the value of x in (2)

=) 2(1+4y/3)=y+5

=) 2+8y/3=y+5

=)2+8y= 3y+15

=) 8y-3y= 15-2

=) 5y= 13

=)y= 13/5

Putting y= 13/5 in (1)

=) 3x= 1+4y

=)3x= 1+4(13/5)

=)3x= 1+52/5

=)3x= 5+52/5

=)3x= 57/5

=)15x= 57

=)x= 57/15

=)x= 19/5

[CROSS-MULTIPLICATION]

$= > \frac{x}{ \frac{ - 4}{ - 1} \times \frac{ - 1}{ - 5} } = \frac{y}{ \frac{3}{2} \times \frac{ - 1}{ - 5} } = \frac{1}{ \frac{3}{2} \times \frac{ - 4}{ - 1} } \\ \\ = > \frac{x}{ - 4 \times ( - 5) - 1} = \frac{y}{ - 2 \times - ( - 15)} = \frac{1}{ - 3 - ( - 8)} \\ \\ = > \frac{x}{20 - 1} = \frac{y}{ - 2 + 15} = \frac{1}{ - 3 + 8} \\ \\ = > \frac{x}{19} = \frac{y}{13} = \frac{1}{5} \\ \\ = > \frac{x}{19} = \frac{1}{5} \: \: or \: \: \frac{y}{13} = \frac{1}{5} \\ \\ = > 5x = 19 \: \: or \: \: 5y = 13 \\ \\ = > x = \frac{19}{5} \: \: or \: y = \frac{13}{5}$

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