Question

Solve by substitution method and elimination method.
1. 2x + 3y =5; x-2y =3
2. 5x+ 3y =35; 2x+4y=28

Answer 1

$\sf\huge\bold{\underline{\underline{{Solution}}}}$

1.2x+3y=5 & x-2y=3

By substitution method

x= 3+2y---(1)

2x+3y=5

from equation 1

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

=>6+4y+3y=5

=>6+7y=5

=>7y= 5-6

=>7y= -1

=>y = -1/7

X= 3+2y

x= 3+2(-1/7)

x= 3-2/7

x= 21-2/7

x= 19/7

y = -1/7

By elimination method

2x+3y=5---(×1)

x-2y=3------(×2)

New Equation obtained:

2x+3y=5

2x-4y=6

$(-)(+)\:(-)$

_________

7y= -1

y= -1/7

2x+3y=5

2x-3/7=5

2x=5+3/7

2x=38/7

x= 38/14= 19/7

x= 19/7

_________________________________________________

2.5x+3y= 35 & 2x+4y=28

By substitution method:

5x= 35-3y

x= 35-3y/5----(1)

2x+4y=28

from equation 1

=>2(35-3y/5)+4y=28

=>70-6y/5+4y= 28

=>70-6y+20y=140

=>14y= 140-70

=>14y= 70

=>y= 70÷14=5

y= 5

X= 35-3y/5

x= 35-15/5

x= 20/5

x=4

By elimination method

=>5x+3y=35---(×2)

=>2x+4y=28----(×5)

New Equation obtained

10x+6y=70

10x+20y=140

$(-)(-)\:(-)$

__________

-14y= -70

y= 5

=>5x+3y=35

=>5x+15=35

=>5x=20

x=4